0rthodontist said:This can be done with generating functions if you know them.
1. Find the generating function for 1, 3^2, 3^4, ...
2. From this, find the generating function for 1, 2*3^2, ...
3. Find the generating function for (n+2)*3^(2(n+1)), (n+3)*3^(2(n+2)), ...
4. Subtract the latter from the former and evaluate at 1.
shmoe said:You might find it easier to try and sum:
[tex]1+2x^2+3x^4+\ldots+(n+1)x^{2n}[/tex]
It's not quite a geometric series, but can you turn it into one?
0rthodontist said:Okay--what sums can you do that might be relevant?