Geometric series/ sum to infinity help

For 1a) what did you get for r?
Then use
|r| < 1

Reply 4

ThiagoBrigido

17

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

(edited 4 years ago)

Reply 5

...

(edited 4 years ago)

Reply 6

username5143542

OP

9

Original post by mqb2766

For 1a) what did you get for r?
Then use
|r| < 1

I got r= -2x

Reply 7

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

2b) Use ar^(n-1)

Reply 8

Original post by wherethemangoos

I got r= -2x

So solve
|-2x| < 1

Reply 9

Original post by BuddyYo

1 a) i

Hints not solutions.
Pls delete

Reply 10

Original post by mqb2766

Hints not solutions.
Pls delete

Is that a rule? I didn't know.

Reply 11

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.

Reply 12