Let f(x)=∑n=1∞(x−2)nn5nf(x) = \sum_{n=1}^{\infty} \frac{(x-2)^n}{n 5^n}f(x)=∑n=1∞n5n(x−2)n. Find the interval of convergence of its derivative f′(x)f'(x)f′(x).
[−3,7)[-3, 7)[−3,7)
(−3,7)(-3, 7)(−3,7)
[−3,7][-3, 7][−3,7]
(−3,7](-3, 7](−3,7]