# Geometric series/ sum to infinity help

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#1
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.
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4 weeks ago
#2
What is the condition for convergence, and what is the formula for the infinite sum?
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#3
(Original post by dextrous63)
What is the condition for convergence, and what is the formula for the infinite sum?
Convergence-when r is smaller than one.
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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4 weeks ago
#4
For 1a) what did you get for r?
Then use
|r| < 1
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4 weeks ago
#5
(Original post by 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.
For this series to exist the limit of convergence follows the condition that | 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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4 weeks ago
#6
...
Last edited by BuddyYo; 4 weeks ago
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#7
(Original post by mqb2766)
For 1a) what did you get for r?
Then use
|r| < 1
I got r= -2x
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4 weeks ago
#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)
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4 weeks ago
#9
(Original post by wherethemangoos)
I got r= -2x
So solve
|-2x| < 1
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4 weeks ago
#10
(Original post by BuddyYo)
1 a) i
Hints not solutions.
Pls delete
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4 weeks ago
#11
(Original post by mqb2766)
Hints not solutions.
Pls delete
Is that a rule? I didn't know.
1
4 weeks ago
#12
(Original post by BuddyYo)
Is that a rule? I didn't know.
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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4 weeks ago
#13
(Original post by 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.
got it thanks!
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#14
(Original post by 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)
Thanks
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#15
(Original post by mqb2766)
So solve
|-2x| < 1
Thanks
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