Find the derivative of the power series f(x)=∑n=0∞xnf(x) = \sum_{n=0}^{\infty} x^nf(x)=∑n=0∞xn for ∣x∣<1|x|<1∣x∣<1.
∑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∞xn−1\sum_{n=1}^{\infty} x^{n-1}∑n=1∞xn−1
∑n=0∞xn+1\sum_{n=0}^{\infty} x^{n+1}∑n=0∞xn+1