Question

Find the sum of the given infinite geometric series.

1 + 2/3 + 4/9 + ...

Answer 1

you are supposed to recognize this as \(1+r+r^2+r^3+...=\sum_{k=1}^{\infty}r^{k-1}=\frac{1}{1-r}\)

Answer 2

can u find the common ratio between them ?

Answer 3

ok.

Answer 4

i never covered this before in my real math. and the guys on this site don't explain anything, so sorry if i ask the same question in a different format

Answer 5

so as @hartnn said, your actual job is to recognize \(r\)
then it is a simple computation like the last one

Answer 6

all of these questions are about summing a "geometric series"
geometric series means something of the form \[a+ar+ar^2+ar^3+...\] where you multiply one term by the common ratio \(r\) to get to the next term

Answer 7

this is more succinctly written is "sigma notation" as
\[a+ar+ar^2+ar^3+..=\sum_{k=1}^{\infty}ar^{k-1}\] or as
\[\sum_{k=0}^{\infty}ar^k\]

Answer 8

and if \(-1<r<1\) you can use
\[\sum_{k=1}^{\infty}ar^{k-1}=\frac{a}{1-r}\]

Answer 9

the reasoning behind it is not too hard to understand, but may be a bit hard to write here
are you using a text?

Answer 10

No, this is online

Answer 11

but i've written down every equation and formula you've given me on here

Answer 12

that figures
but since you are on line if you want to know why the formula works, you can probably get lots of explanation by googling
i would recommend looking here
http://patrickjmt.com/

Answer 13

on the other hand if you are content with the formula i wrote it above
also feel free to post similar questions, no one will be annoyed, and if they are that is their problem

Answer 14

Thanks a ton dude :) I really appreciate the help. much better than my old math teacher could do

Answer 15

yw