If f(x)=∑n=0∞xnf(x) = \sum_{n=0}^{\infty} x^nf(x)=∑n=0∞xn, what is the power series for f′(x)f'(x)f′(x)?
∑n=0∞nxn−1\sum_{n=0}^{\infty} n x^{n-1}∑n=0∞nxn−1
∑n=1∞nxn−1\sum_{n=1}^{\infty} n x^{n-1}∑n=1∞nxn−1
∑n=1∞xnn\sum_{n=1}^{\infty} \frac{x^n}{n}∑n=1∞nxn
∑n=0∞(n+1)xn\sum_{n=0}^{\infty} (n+1) x^n∑n=0∞(n+1)xn