Evaluate the sum (for math nerds)
[tex]i {}^{0!} + i {}^{1!} + i {}^{2!} + i {}^{3!} + ... + i {}^{100!} [/tex]
Note that :
[tex]i = \sqrt[]{ - 1} [/tex]

Answers

Answer 1

Answer: i+96

Step-by-step explanation:

Note that [tex]i^{4k}[/tex], where k is an integer, is equal to 1.

This means that [tex]i^{4!}=i^{5!}=i^{6}=\cdots=i^{99!}+i^{100!}=1[/tex]

So, we can rewrite the sum as [tex]i^{1}+i^{1}+i^{2}+i^3+97(1)=i+i-1-i+97=i+96[/tex]

Answer 2

[tex]n![/tex] is divisible by 4 for all [tex]n\ge4[/tex]. This means, for instance,

[tex]i^{4!} = \left(i^4\right)^{3!} = 1^{3!} = 1[/tex]

[tex]i^{5!} = \left(i^4\right)^{5\times3!} = 1^{5\times3!} = 1[/tex]

etc, so that [tex]i^{n!} = 1[/tex] for all [tex]n\ge4[/tex].

Meanwhile,

[tex]i^{0!} = i^1 = i[/tex]

[tex]i^{1!} = i^1 = i[/tex]

[tex]i^{2!} = i^2 = -1[/tex]

[tex]i^{3!} = i^6 = (-1)^3 = -1[/tex]

Then the sum we want is

[tex]i^{0!} + i^{1!} + i^{2!} + i^{3!} + 97\times1 = i + i - 1 - 1 + 97 = \boxed{95+2i}[/tex]


Related Questions

¿Cómo se dice 80 en números romanos?​

Answers

Answer:

PLEASE MARK ME BRAINLEST...

Step-by-step explanation:

Para leer y escribir correctamente el número 80 como número romano LXXX, debe leerse y escribirse de izquierda a derecha, y de mayor a menor número.

Answer:

Guessing that Romanos means Roman Numerals = LXXX

Step-by-step explanation:

L=50

X=10

10X3= 30

30+50=80

What is the answer to n/4 = -9

Answers

Answer: n=-36

Step-by-step explanation:

Answer:

-36

Step-by-step explanation:

n/4=-9

Can be rewritten as

n/4 x 4 = -9x4

simplify

n=-36

Use this model to calculate
3/8 times 2/6
A.16/18 B.13/24 C.6/48 D5/48

Answers

Answer:

Step-by-step explanation:

i do not see any model, but the answer is

3/8*2/6=6/48

The solution of the expression 3/8 times 2/6 is,

⇒ 6/48

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 3/8 times 2/6

Now, We can simplify as;

⇒ 3/8 times 2/6

⇒ 3/8 × 2/6

⇒ 6/48

Thus, The solution of the expression 3/8 times 2/6 is,

⇒ 6/48

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ3

what is the solution of 4 + √ 5x + 68 = x + 10​

Answers

Answer:X=3

Step-by-step explanation: Option B

Stephen Simmons received a single payment loan for a loan for $6,200. he agreed to repay the loan and 160 days at an interest rate of 10% ordinary interest. What is the maturity value of his loan when he pays it back in 160 days. 

Answers

9514 1404 393

Answer:

  $6475.56

Step-by-step explanation:

The maturity value is ...

  A = P(1 +rt)

where P is the principal amount, r is the annual rate, and t is the number of years. For ordinary interest, a year is 360 days, so the number of years is 160/360 = 4/9.

The loan value is ...

  A = $6200(1 + 0.10×4/9) ≈ $6475.56

Stephen's loan has a maturity value of $6,475.56.

Evilate the functions

f(x+7)=

Answers

Answer:

hindi ko alam pano bayanpasenya na

What equivalent ratio to 5:15?

Answers

Answer:

10 : 30

Step-by-step explanation:

Answer:

10:30

----------------------

math 2 help ummmmmyeah

Answers

Answer:

1. 38 degrees

2. 38 degrees

Step-by-step explanation:

It tells you that angle 1 is 38 degrees, and they are supplementary angles, which means angle 2 is also 38 degrees.

Hope this helps :)

Let me know if there is anything to fix!!

Word problem please help thank you

Answers

Answer:

The equation would be           P(t) = 280t + 3310              

The estimated number of moose in 2008 would be 8350 moose.

Step-by-step explanation:

First we will have to find out by how much will the number of moose increase each year. In order to do that we the number by which the population of moose increase, by the difference between 1991 and 1999. And so we get...

[tex]\frac{5830-3590 }{1999 - 1991} = \frac{2240}{8} = 280[/tex]

Now that we know by how much the number of moose increases each year, we can make the following equation...

Let "t" be the number of years from 1990, then...

P(t) = 280t + 3310

(if you are wondering why is it 3310, it is because you have to put in the number of moose that was there in 1990 and you can get that number by substracting 280 from the number of moose in 1991).

Based on the linear relation we figured out, the number of moose in 2008 would be predicted to be...

P(t) = 280t + 3310

P(2008 - 1990) = 280(2008 - 1990) + 3310

P (18) = 280(18) + 3310

P(18) = 8350

I have 21 students and each picture takes 3 minutes and each class picture takes 10 minutes

Answers

Answer:

It would take 73 minutes in total.

Step-by-step explanation:

21 students x 3 minutes = 63 minutes

63 + 10 = 73

I hope this is what you were asking :)

The zoo charges $14.50 for each visit, or you can buy a membership for $100

Answers

Answer:

Step-I’m going to need more information

Answer:

ill rather buy the membership

Step-by-step explanation:

Because its less money for more times to go to the zoo.

6p² equals to..................​

Answers

Answer:

36p is the correct answer

2. Izza walked 5 steps forward, 8 steps backward, 9 steps forward and 3 steps backward. How
many steps is Izza from where she started?
3. Samuel was at the ground floor when he decided to go to the fourth floor. He then went down 2
or and went up 7 more floors. Where is he now?
On a winter night the temperature dropped f.rom -6°C to -15°C. How many degrees did the
Tamperature drop?​

Answers

Answer:

Izza walked 3 steps forward

samuel is on the 9th floor

-9 degrees

Step-by-step explanation:

For the sequence defined by a1=2

An+1=5/an-4

Answers

Answer:

i thnk is 239.213

Step-by-step explanation:

Please help this is due today!

Calculate the unknown missing angle measures.

Do not answer this with one answer ,blank, or a ridiculous answer.... this is serious please.

Answers

Answer:

well it is a right trianlg that means that the first side is 90 degrees

and the other two sides are 45 because they look the same angles so 180 minus 90 = 90 divide that by 2 to get 45

Step-by-step explanation:

Help pls!!!!!!!!!!!!!!!!!!!!!!!!! Questions 2 Five students scored 80 on a test, five students scored 85, and five students scored 90.
Complete each statement below by inserting the correct number
a. The mean is equal to
b. The median is equal to
C. The range is equal to
d. The mean absolute deviation is equal to

Answers

Answer:

Ñ consigo responder pois estar em inglês

Find the m AB
X
34°
B
34°
68°
146°
56°

Answers

Answer:

68°

Step-by-step explanation:

Given

<AXB = 34 °

Arc AB = 2 * <AXB ( Relation between arc and inscribed angle)

Arc AB = 2 * 34°

= 68°

Hope it will help :)

12 x satisfies the inequality: 2x -8 < 12

Create an inequality to represent all the possible values of x.




Answers

Answer:  x<10

Step-by-step explanation:

2x-8<12

2x-8+8<12+8

2x<20

[tex]\frac{2x}{2}[/tex]<[tex]\frac{20}{2}[/tex]

x<10

Please help this is due today!

Use the diagram to complete the statements using correct notation. If there is not enough information to prove congruency, explain why:

Example cannot be determined

If it’s a congruent, the congruence reason has to be SAS SSS ASA OR SAA

Do not answer this with one answer ,blank, or a ridiculous answer.... this is serious please.

Answers

Answer:

Can not be determined.

Step-by-step explanation:

From the figure attached,

In ΔHFS and ΔIFS,

Side HS ≅ Side HI [Given]

∠HFS ≅ ∠IFS [Given]

Side FS ≅ Side FS [Reflexive property]

But there is no property of SSA (Side-side-angles for the congruence of two triangles)

Therefore, answer is "can not be determined".

What expression simplifies to 2i ? help asap lots of points

Answers

Answer:

Step-by-step explanation:

First, consider the following expression.

(6x + 8) + (4x + 2)

To simplify this expression, you combine the like terms, 6x and 4x. These are like terms because they have the same variable with the same exponents. Similarly, 8 and 2 are like terms because they are both constants, with no variables.

(6x + 8) + (4x + 2) = 10x + 10

The absolute value of the complex number, 2i, is 2. We can put the complex number, 2i, in the form a + bi by letting a = 0.

please tell fast plzzzzzz​

Answers

Step-by-step explanation:

1x+4x=180(sum of supplementary angles)

5x. =180

x. =180/5

x. = 36

Use the tangent to find the length of side PR.Express your answer to the nearest tenth.

Answers

Answer:

PR = 4.9

Step-by-step explanation:

For given angle Q, RQ is the adjacent leg, and PR is the opposite leg.

We recall the meaning of the tangent ratio.

tan A = opp/adj

Here we have

tan Q = opp/adj

tan 51 deg = PR/4.0

PR = 4.0 * tan 51 deg = 4.9

Answer: PR = 4.9

21 x 15 = (20 + 1) x 15 =

Answers

Answer:

hello! have a good day!

21 x 15 = (20 + 1) x 15 = 315

plecorato de potasio es elemento

Answers

Answer:

no es un elemento de la tabla periódica

please help me thank you

Answers

Answer:

y+3=-3/5(x + 5)

Step-by-step explanation:

3x+5y=15 has a slope of -3/5. With the point (-5,-3) that would be y + 3= -3/5(x + 5) in point slope form.

Can you please help me
Step-by-step explanation please

Answers

Answer:

x=9

Step-by-step explanation:

It’s a ratio.

2/6=5/(6+x)

cross-multiply

12+2x=30

2x=30-12

2x=18

x=9

Or even more simply:

2/6=3/x

2x=18

x=9

A bank pays 3.4% annual interest,
compounded monthly. If $1550 is invested
for 11 years, what will be the ending value
of the account?

Answers

Answer:

$2,251.79.

total compound should be is $701.79.

Step-by-step explanation:

A explanation would help very much

Answers

Answer:

x = 14

y = 40

Step-by-step explanation:

3y+8 = 128

3y = 120

y = 40

45/20=2.25 (scale factor)

5x-25 = 2.25(2x-8)

5x-25 = 4.5x - 18

.5x = 7

x=14

I need the answer asap!!

Answers

Answer:

Step-by-step explanation:

x² × 2x² = 2x^4 (2x to the power of 4)

x² × -3x = -3x³

+3 × 2x² = 6x²

+3 × -3x = -9x

2x^4    ,     -3x³    ,   6x²,      -9x

In bold are the bottom two

if a Biro costs 12.50naira. How many biros can buy with 300 naira?​

Answers

Answer:

300\12.50

Step-by-step explanation:

that will be your answer bra

Other Questions
If the greatest value the variable m can be is less than 9, which of the following inequalities best shows all the possible values of m? m < 9 m > 9 m 9 m 9 The marks obtained by 10 student in a test are as follows: 3,7,6,2,8,5,9,1,4 and 10. find the mean mark The volume of a rectangular box is 1.0 ft3. what is the length if the width is 1.0 ft and the height is 1.5 ft? HELP ME PLEASELOOK AT IMAGE explain why x squared = 16 has two solutions. What are the solutions. I need help with the slope The Lunar Module could make a safe landing if its vertical velocity at impact is 2.8 m/s or less. Use conservation of energy to determine h in each case. The acceleration due to gravity at the surface of the Moon is 1.62 m/s2.Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is zero.Express your answer to two significant figures and include the appropriate units.Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is 1.7 m/s downward.Express your answer to two significant figures and include the appropriate units.Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is 1.7 m/s upward.Express your answer to two significant figures and include the appropriate units. A machine fills bags with sweets there are 4275 sweets there are 28 sweets in each full bag the machine fills as many bags as possible how many sweets are left must show your working Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why. The following table shows Kamals bank account balance after 7 months. *TABLE IN THE FILE ATACHED BELOW*a) What is the rate of change? Show your work.b) What does the rate of change mean in Kamals scenario?c) What is the initial value?d) What does the initial value represent in Kamals scenario?e) Determine the equation of the linear relation which represents his bank account balance.PLEASE HELP I DON'T HAVE ANY TIME On Monday the change in the value of one share of a companies stock cant be represented as -$2.85 Tuesday the value of one share of the companies that changes again which of these describes a situation that would bring the total change for the two days to zero dollars If you can not see something with your eyes you can increase the _____ to make it look bigger. PLEASE HELP THANKSS-How does a heterogeneous mixture differ from a homogeneous mixture? How are they similar? A neurotransmitter binds to a metabotropic receptor and pka is ultimately activated, which type of neurotransmitter likely bound? HELP PLEASE!!! I know how important it is to care for our environment. And I know building a recycling center seems like a great idea, but it is not. Building a recycling center is like trying the bath to bathe a cat. It is a lot of work, and by the end nothing is any cleaner. What rhetorical device is being used in this presentation?A. MetaphorB. Rule of threeC. RepetitionD. Simile A(n) ________ is information that is passed to a function, and a(n) ________ is a special variable that receives and holds that information. Read This living hand, now warm and capable by John Keats. Based on what you have learned about literary movements, which movement does this poems form and elements fit best?This living hand, now warm and capableOf earnest grasping, would, if it were coldAnd in the icy silence of the tomb,So haunt thy days and chill thy dreaming nightsThat thou would wish thine own heart dry of bloodSo in my veins red life might stream again,And thou be conscience-calmdsee here it isI hold it towards you.NaturalismRomanticismRealismClassicism True or false: sensitivity differences during light and dark adaptation result, at least in part, from the difference in bleaching and regeneration rates of photopsin and rhodopsin. Citrus Corporation is a calendar year S corporation with the followingcurrent year information:Operating lossLiabilities:$(2,160,000)Notes payable, Big Apple Bank360,000Notes payable, Grapefruit (individual) 360,000On January 1, Orange (an individual) bought 50% of Citrus Corporationstock for $540,000. How much of the operating loss may Orange deductcurrently? Assume the excess business loss limitation does not apply. I don't understand any recursive sequences please help explain so The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct?A).Both the domain and range of the transformed function are the same as those of the parent function.B).Neither the domain nor the range of the transformed function are the same as those of the parent function.c).The range of the transformed function is the same as the parent function, but the domains of the functions are different.D).The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.