Determine the interval of convergence for ∑n=1∞(x−3)nn⋅2n\sum_{n=1}^{\infty} \frac{(x-3)^n}{n \cdot 2^n}∑n=1∞n⋅2n(x−3)n.
(1,5)(1, 5)(1,5)
[1,5)[1, 5)[1,5)
(1,5](1, 5](1,5]
[1,5][1, 5][1,5]