Need help finding the sum of a sequence

[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 don't know of the integrate when I have ^(2n), and not only n.

please help

 

[Office_Shredder]

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

 

[HallsofIvy]

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!

 

[hyper]

How should I find the sum then?

 

[tim_lou]

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