I need to find the closed-form solution to the following problem. I'm not really sure how to do the summation of a geometric sequence. Anyways, here it is:

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- Feb 17th 2010, 08:23 PMNeodymiumSummation of a geometric sequence
I need to find the closed-form solution to the following problem. I'm not really sure how to do the summation of a geometric sequence. Anyways, here it is:

- Feb 17th 2010, 09:40 PMDrexel28
- Feb 18th 2010, 12:05 AMNeodymium
I'd like to take a guess but I honestly don't have a clue on how to do this. At all.

- Feb 18th 2010, 11:40 AMDrexel28
- Feb 18th 2010, 02:05 PMSoroban
Herlo!

I believe Drexel128 meant: .

I found it like this . . .

From: .

. . we have: .

Subtract [2] - [1]:] .

. . . and we have: .

Let: .

Then [3] becomes: .

Divide by

The generating function has the form: .

We know the first two terms of the sequence:

. .

Sugbtract [2] - [1]: .

Sustitute into [1]: .

Hence, the function is: .

. . Therefore: .

- Feb 18th 2010, 02:10 PMDrexel28