Determine the interval of convergence for ∑n=1∞(x−2)nn⋅2n\sum_{n=1}^{\infty} \frac{(x-2)^n}{n \cdot 2^n}∑n=1∞n⋅2n(x−2)n. Test endpoints carefully.
0<x<40 < x < 40<x<4
0≤x≤40 \le x \le 40≤x≤4
0≤x<40 \le x < 40≤x<4
0<x≤40 < x \le 40<x≤4