# Thread: Power Series Differentiation & Integration

1. ## Power Series Differentiation & Integration

Hi,

the question asks for the derivative of

Sigma notation (n=0) [(2nx^n) / (2n+1)]

Is it just f'(x) = 2(n^2)(x^(n-1))?

The second part asks for the integral of the above power series so that F(0) = 0?

2. Originally Posted by shogunhd
Hi,

the question asks for the derivative of

Sigma notation (n=0) [(2nx^n) / (2n+1)]

Is it just f'(x) = 2(n^2)(x^(n-1))?

The second part asks for the integral of the above power series so that F(0) = 0?
yes, but don't forget the denominator..

note: A power series can be differentiated/integrated term by term over any closed and bounded interval inside the radius of convergence..