Need help finding the sum of a sequence

1. Nov 3, 2008

hyper

I have to sequence 2*(n-1)*x^(2n), I have tried integrating and then finding the sum and then derivating the sum, and I allmost get the right answer.

But I think I am integrating wrong since I really dont know of the integrate when I have ^(2n), and not only n.

2. Nov 3, 2008

Office_Shredder

Staff Emeritus
When you integrate x2n Just write k=2n. Then integral of xk is xk+1/(k+1) = x2n+1/(2n+1)

3. Nov 3, 2008

HallsofIvy

Staff Emeritus
You know, I presume, that the integral of xn is 1/(n+1) xn+1+ C where n can be any number. Well, 2n is just a number! The integral of x2n is 1/(2n+1) x2n+1+ C. So the integral of 2(n-1)x2n is 2((n-1)/(2n+1))x2n+1. But I don't think that will help you find the sum!

4. Nov 3, 2008

hyper

How should I find the sum then?

5. Nov 3, 2008

tim_lou

differentiate sum x^2n and see what you get. Or better yet, differentiate x^(2(n-1))