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:
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: .