What is the result of differentiating the series f(x)=∑n=1∞xnnf(x) = \sum_{n=1}^{\infty} \frac{x^n}{n}f(x)=∑n=1∞nxn term-by-term?
∑n=1∞xn−1\sum_{n=1}^{\infty} x^{n-1}∑n=1∞xn−1
∑n=1∞nxn−1\sum_{n=1}^{\infty} n x^{n-1}∑n=1∞nxn−1
∑n=0∞xn\sum_{n=0}^{\infty} x^n∑n=0∞xn
∑n=1∞xn−1n2\sum_{n=1}^{\infty} \frac{x^{n-1}}{n^2}∑n=1∞n2xn−1