# Geometric series/ sum to infinity help

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1. Given that the geometric seriea 1-2x+4x^2-8x^3+... is convergent,

a) find the range of possible values of x

b)find an expression for S(infinity) in terms of x

2. In a convergent geometric series the common ratio is r and the first term is 2,

Given that S(infinity)=16×S3

A) find the value of the common ratio, giving your answer (4 s.f)

b) find the value ofthe fourth term

Thankyou, Ive been trying but I dint get the answer.

a) find the range of possible values of x

b)find an expression for S(infinity) in terms of x

2. In a convergent geometric series the common ratio is r and the first term is 2,

Given that S(infinity)=16×S3

A) find the value of the common ratio, giving your answer (4 s.f)

b) find the value ofthe fourth term

Thankyou, Ive been trying but I dint get the answer.

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#2

What is the condition for convergence, and what is the formula for the infinite sum?

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(Original post by

What is the condition for convergence, and what is the formula for the infinite sum?

**dextrous63**)What is the condition for convergence, and what is the formula for the infinite sum?

Infinite sum- a over 1- r.

Ive solved 1.b, but I cant get 1.a. Also I solved 2.

Last edited by wherethemangoos; 4 weeks ago

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#5

(Original post by

1. Given that the geometric seriea 1-2x+4x^2-8x^3+... is convergent,

a) find the range of possible values of x

b)find an expression for S(infinity) in terms of x

2. In a convergent geometric series the common ratio is r and the first term is 2,

Given that S(infinity)=16×S3

A) find the value of the common ratio, giving your answer (4 s.f)

b) find the value ofthe fourth term

Thankyou, Ive been trying but I dint get the answer.

**wherethemangoos**)1. Given that the geometric seriea 1-2x+4x^2-8x^3+... is convergent,

a) find the range of possible values of x

b)find an expression for S(infinity) in terms of x

2. In a convergent geometric series the common ratio is r and the first term is 2,

Given that S(infinity)=16×S3

A) find the value of the common ratio, giving your answer (4 s.f)

b) find the value ofthe fourth term

Thankyou, Ive been trying but I dint get the answer.

**| r | < 1,**. Notice that from the partial sum formulae

**S=a(1-r^n)/(1-r)**you can also derive the formula when the limit: n approaches infinity which is

**S=a/1-r**

Last edited by ThiagoBrigido; 4 weeks ago

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#8

for 2 a) Just calculate S3 in terms of r and then equate it with the S(infinity) formula

2b) Use ar^(n-1)

2b) Use ar^(n-1)

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#12

(Original post by

Is that a rule? I didn't know.

**BuddyYo**)Is that a rule? I didn't know.

The aim is to let the original poster do as much as possible themselves, and make mistakes to learn.

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#13

(Original post by

No problem, see the sticky at the top of the forum about responding to questions.

The aim is to let the original poster do as much as possible themselves, and make mistakes to learn.

**mqb2766**)No problem, see the sticky at the top of the forum about responding to questions.

The aim is to let the original poster do as much as possible themselves, and make mistakes to learn.

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(Original post by

for 2 a) Just calculate S3 in terms of r and then equate it with the S(infinity) formula

2b) Use ar^(n-1)

**BuddyYo**)for 2 a) Just calculate S3 in terms of r and then equate it with the S(infinity) formula

2b) Use ar^(n-1)

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