Question

Find the sum of the following infinite geometric series if it exists 1/2 + -1/4 + 1/8 + -1/16

Answer 1

We have x/y^2 .
OK ?!

Answer 2

But in each 2th we have (-) too !

Answer 3

I know the common ratio is -1/2

Answer 4

So what do you want ?!!!

Answer 5

the sum of it

Answer 6

In an arithmetic series I can find the sum of that but is there a formula for finding the sum of a geometric series?

Answer 7

-0/1

Answer 8

What does that mean?

Answer 9

YES !
LOOK :

Answer 10

?....

Answer 11

Number.(end.first)/2

Answer 12

how do you find the last number?

Answer 13

You have it !
You want a way to find the sum .HA?
It s a way to find that .!

Answer 14

There is no last number if it's infinite?

Answer 15

I thought I was suppose to use sigma somehow?

Answer 16

You want nth ?
OK ?

Answer 17

What?

Answer 18

I just want to find the sum of the infinite geometric series if it's possible? -.-

Answer 19

and I don't know how to

Answer 20

I don't understand what you are trying do..

Answer 21

In this you want to find the
n th
Number .
Right ?

Answer 22

what is the nth number?

Answer 23

Amm for example when we say 2th day ...
It s n th Number !

Answer 24

No i dont want the nth number i want the sum of the entire infinite series..

Answer 25

I can get the nth number but it asks for no nth number.

Answer 26

it asks for the entire sum of the infinite geometric series.

Answer 27

for a GP with first term 'a' and common ratio r less than 1 the sum for infinite terms is\[\frac{ a }{ 1-r } = S_n\]
it is derived from applying the infinite limit to the formula for the sum of n terms.

Answer 28

how do you get the sum of infinite terms?

Answer 29

Does that equation equal the sum?..

Answer 30

yes S_n is the sum of the infinite GP

Answer 31

Then would it be 1/3?..

Answer 32

Correct, the sum is \[\frac{ 1/2 }{ 1-(-1/2) } = \frac{1/2}{3/2}= \frac{1}{3}\]

Answer 33

Okay. Thanks.