Mathematics High School

Use the geometric series f(x) = 1/1 - x = sigma^infinity_k = 0 x^k, for |x| < 1. to find the power series representation for the following function (centered at 0). Give the interval of convergence of the new series. g(x) = x^3/1 - x Which of the following is the power series representation for g(x)? A. sigma^infinity_k = 0 x^3/x^k C. sigma^infinity_k = 0 1/1 - x^k + 3 B. sigma^infinity_k = 0 x^k + 3 D. sigma^infinity_k = 0 x^3k The interval of convergence of the new series is. (Simplify your answer. Type your answer in interval notation.)

Answers

Answer 1

B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

To find the power series representation for g(x), we need to rewrite g(x) in terms of the given geometric series.

Notice that g(x) can be written as:
g(x) = x^3/1 - x = x^3 * (1/1-x)

We can now substitute the formula for the geometric series to get:

g(x) = x^3 * sigma^infinity_k = 0 x^k
= sigma^infinity_k = 0 (x^3 * x^k)
= sigma^infinity_k = 0 x^(k+3)

Therefore, the power series representation for g(x) is:
sigma^infinity_k = 0 x^(k+3)

The interval of convergence of this series is the same as that of the geometric series, which is |x| < 1.

In interval notation, this can be written as (-1, 1).

Therefore, the correct answer is B. sigma^infinity_k = 0 x^k + 3, and the interval of convergence is (-1, 1).

Know more about convergence here:

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Related Questions

What is the equation graph below?

Answers

Answer: y =7/4x

Step-by-step explanation:

The y-intercept is 0. To find the slope, do the change in y over the change in x. At the point on the graph, there is a slope of 14/8 = 7/4

a coin is tossed several times and the ratio of the head to tails is 24:26. What Fraction of Tosses are heads?

Answers

Answer:

siiiiiiiiii

Step-by-step explanation:

It takes lucas 3 hours to cycle from his home to his friend's village. But if he travels 5 mph slower, it will take him 1.5 hours longer. How far is the friend from lucas' house

Answers

Answer:

Step-by-step explanation:

It takes Lucas 3 hours to cycle from his home to his friend’s village:  

3 hours • (a certain speed) = distance in miles  

If he travels 5mph slower, it will take him 1.5 hours longer:

4.5 hours • (the same speed - 5mph) = the same distance in miles

 4.5 • (x - 5) = 3x

4.5x - 22.5 = 3x

1.5x = 22.5

x = 15mph  

3hours • 15mph = 45 miles

Please Help i need this right now Thanks

Answers

60° i think but i’m not sure

What is -2 1/3 - (-5)?

Answers

Answer: =2  2/ 3

Step-by-step explanation:

Please help I don't know how to do this

Answers

i not sure but i think its  183

Answer:

question 18 asking for a equation for each week 89÷4

question 19 would be 60 + 123 = 183 then 183 ÷ 4 = 45.75

(2x2)+(6x 109)
I don’t know how to do this

Answers

Answer:

658

Step-by-step explanation:

4+654=658.........

Answer:

658

Step-by-step explanation:

First solve 2x2, which is equal to 4.

Then solve 6 x 109 which is equal to 654.

Now add 4 to 654, and you'll get 658

John joined a gym for 6 months. He pays 20$ per month plus a membership fee. If his bill is 150$, what was the membership fee?

Answers

Answer:

Step-by-step explanation:

If he's been at the gym for 6 months, and he is charged $20 each month, then he has paid $120 dollars, not counting his membership fee. His total bill is $150.

150-120= $30

His membership fee was $30.

Hope this helps!

Mark Brainliest plz!

x is the number of months and y is the membership fee

[tex]cost = 20x + y[/tex]

[tex]150 = 20(6) + y[/tex]

[tex]150 = 120 + y[/tex]

[tex]150 - 120 = 120 - 120 + y[/tex]

[tex]30 = y[/tex]

The membership fee was $30.

Solve the equation. 8w = 48​

Answers

Answer:

8w=48

This answer can be simplified by dividing both sides which contain the variable, which in this case is 8. Dividing 48 by 8 gets 6. This means that w equals 6.

Answer:

w = 6

Step-by-step explanation:

Solve

8w = 48

8w/8 = 48/8

= w = 6

x is an even whole number less than 5.​

Answers

Answer:

x can either be 2 or 4

Step-by-step explanation:

Whole numbers less than 5 are = 1, 2, 3, 4

Even whole numbers less than 5 are = 2 and 4

1 and 3 are odd numbers

Therefore, even whole number less than 5 are 2 and 4

x can either be 2 or 4

Find the area of a triangle with:
b: 14 cm
h: 23 cm
ANSWERS
322 cm2
322 cm3
161 cm2
161 cm3

Answers

Answer:

161cm2

Step-by-step explanation:

Area: 1/2 x base x height

1/2 x 14 x 23=161

Area is measured in cm2

Hope this helps!

Today, everything at the store is on sale. The store offers a 20% discount. The regular price of a T-shirt is $16. What is the discount price?

Answers

Answer:

12.8

Step-by-step explanation:

I think it is $14 or $4 one of those I did 20-16=4 but I’m not sure if it is - or times if it is times it will be $14 good luck:)

Perform the indicated operation.
f (x) = x2 − 4 g(x) = −3x Find f (g(x))

Answers

Answer:

-6x-4

Step-by-step explanation:

2(-3x)-4

-6x-4

r F(x) is your frame function since it is on the outside, when every you get to an x in the F function you plug in the G function then solve as normal.

what times 1,000 equals 4,320

Answers

Answer:

4.32

Step-by-step explanation:

Call the unknown number = x

We have: 1000x = 4320

=> x = [tex]\frac{4320}{1000}[/tex] = 4.32

=> The number we need to find is 4.32

Answer:

4.32

Step-by-step explanation:

The circumference of a circle is 5 feet. What is the area?
Give the exact answer in simplest form.

Answers

Answer:

We have the formula for the area of a circle: S = R² x [tex]\pi[/tex]

=> S = 5² x 3.14 = 78.5 f²

Step-by-step explanation:

6/1000 as a common fraction

Answers

This question isnt rlly descriptive but 6/1000 could be 3/500?

pls help me solve surds , √75 ,√48, √12,√125,√28. pls help​

Answers

√75 = √(5²×3) = √5² √3 = 5√3 = 8.66

√48 = √(4²×3) = √4² √3 = 4√3 = 6.93

√12 = √(2²×3) = √2² √3 = 2√3 = 3.46

√125 = √(5²×3) = √5² √3 = 5√3 = 11.18

√28 = √(2²×7) = √2² √7 = 2√7 = 5.29
All the answers are rounded off to the nearest hundredth.

√75 = 5√3 = 8.66

√48 = 4√3 = 6.93

√12 = 2√3 = 3.46

√125 = 5√5 = 11.18

√28 = 2√7 = 5.29

9. An inequality is shown
2x - 5 < 33
Select all the values that are solutions to this inequality
a. 28
b. 26
C. 19
d. 18
e. 12

PLEASE HELPP!!

Answers

The answer is c 19
38/2=19
Step-by-step explanation
The answer is d. 18 and e. 12.

Explanation:

2x - 5 < 33

2x < 33 + 5

2x < 38

x < 38/2

x < 19

x must be smaller than 19.

It can’t be 19 because it didn’t say smaller than or equal to.

So the answer is 18 and 12.


HELP ASAP DUE IN 20 MINUTES

Answers

Answer:

x = 3

< D = 26

< E = 54

Step-by-step explanation:

I did the math

Silas and Lilly attended a math conference. The total registration fee was $327.50. If each person paid the same amount, which equation
represents the amount each person paid?
A 2x = 327.50
B 1/2x = 327.50
C x + 2 = 327.50
D x - 2 = 327.50

Answers

Answer:I think the answer is letter B.

Step-by-step explanation:

What fraction do you multiply 3 by to get 1

Answers

the answer is 1/3

1/3 + 1/3 + 1/3 equals 1

which is the same as 1/3 times 3

The length of a rectangle is 5cm and the width is 3cm. What is the length of a diagonal? Leave the answer in reduced exact form. Hint: Draw A PICTUR



​

Answers

Answer:

[tex]\sqrt{34} } =5.83[/tex]

Step-by-step explanation:

[tex]D=\sqrt{5^{2} +3^{2} } =\sqrt{34}[/tex]

If the lines in a system of equations have different slopes and the same y-intercept, how many solutions does the system have?

Answers

Answer:

289819

Step-by-step explanation:

help plsss how do you find the size of angle ABE​

Answers

Answer:

∠b = 90°

Step-by-step explanation:

If you wrote it correctly then ∠d will = 90°, right?

We have AB ║(which is parallel to) D => ∠b = ∠d = 90°

P/S: I think that you took the wrong photo, the right question should be above. I'm very please if you can take it again and I will write the right solution down below in the comment section (if u don't mind)

Write the following inequality in slope-intercept form. –12x – 2y ≥ –42 y ≥ –6x – 21 y ≤ –6x – 21 y ≤ –6x + 21 y ≥ –6x + 21

Answers

Answer:

y ≤ –6x + 21

Step-by-step explanation:

por liquidación,toda la ropa de invierno está en oferta,te descuentan 50 pesos por cada 100 pesos que compres ¿cuanto se deberá pagar por una chamarra cuyo precio y otal es de 850 pesos?​

Answers

Answer:

no comprendo

Step-by-step explanation:

Find the length of side a.
10
A
6
A. 4
B. 64
C. V 136
D. 8
PREVIOUS

Answers

Answer:

D .8

Step-by-step explanation:

hypotenuse (h) = 10

base (b) = 6

perpendicular (p) = a= ?

We know by using Pythagoras theorem we get

p = √ h² - b²

a = √ 10² - 6²

a = √ 64

a = 8

Hope it will help :)

SOMONE HELP PLEASE! I HAVE BEEN STRUGGLING ALL DAY!

Answers

Answer: 378 the second option

Step-by-step explanation:

Answer:

378

Step-by-step explanation:

Multiply 9 and 12 then divide by 2 to get the area of the triangle then multiple by 7 to get the volume

determine if f (x) = - x^3 + 4x^2 +7x - 6

Answers

-x(x2-4x-7)+6=-x(x2-4)-7+6=-x(x+2)(x-2)-1=-x-1

PLEASE HELP! WILL MARK BRAINLIEST IF U ANSWER CORRECTLY! IF WRONG U WONT GET IT

Answers

Answer: 120cm

Step-by-step explanation:

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