Hey MSUMathStdnt.

Given the convergence criteria the sum should be 3 - (1/[1+1/3]) = 3 - 3/4 = 12/4 - 3/4 = 9/4

Results 1 to 3 of 3

- December 15th 2012, 08:42 PM #1

- Joined
- Feb 2010
- From
- New Jersey
- Posts
- 80

## Sum 3-1+1/3-1/9+...=9/4

I have numerically verified that the following sum comes to , the same thing the back of the book says. So what'd I do wrong?

Find the sum of the convergent series

.

I verified that the above sum can be represented as

,

which can be rewritten as

.

I believe I can apply the geometric series to the summation, giving me

.

Ahhh... but now I see that the geometric series equation starts the summation at (do you find that typing up your answers sometimes helps you realize what's wrong? Why is that?).

So, I need to subtract from my answer, which (unsurprisingly) gives .

- December 15th 2012, 10:56 PM #2

- Joined
- Sep 2012
- From
- Australia
- Posts
- 5,024
- Thanks
- 1101

- December 16th 2012, 04:08 AM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,024
- Thanks
- 832