Mathematics College

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

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

Answers

Answer:X=3

Step-by-step explanation: Option B

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

What equivalent ratio to 5:15?

Answers

Answer:

10 : 30

Step-by-step explanation:

Answer:

10:30

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

please tell fast plzzzzzz

Answers

Step-by-step explanation:

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

5x. =180

x. =180/5

x. = 36

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

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 :)

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:

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:

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.

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.

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".

Evilate the functions

f(x+7)=

Answers

Answer:

hindi ko alam pano bayanpasenya na

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 :)

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

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

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

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

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

¿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

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

Answers

Answer:

hello! have a good day!

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

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 ...

Answer:

no es un elemento de la tabla periódica

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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]​

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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]