If f(x)=∑n=0∞cnxnf(x) = \sum_{n=0}^{\infty} c_n x^nf(x)=∑n=0∞cnxn, what is f′(x)f'(x)f′(x)?
∑n=0∞cnxn−1\sum_{n=0}^{\infty} c_n x^{n-1}∑n=0∞cnxn−1
∑n=1∞n⋅cnxn−1\sum_{n=1}^{\infty} n \cdot c_n x^{n-1}∑n=1∞n⋅cnxn−1
∑n=1∞cnxn\sum_{n=1}^{\infty} c_n x^n∑n=1∞cnxn
∑n=0∞cnxn+1\sum_{n=0}^{\infty} c_n x^{n+1}∑n=0∞cnxn+1