Consider the sequence an=n⋅xn−1a_n = n \cdot x^{n-1}an=n⋅xn−1. For what range of xxx does the series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an converge?
∣x∣<1|x| < 1∣x∣<1
∣x∣≤1|x| \leq 1∣x∣≤1
x<1x < 1x<1
∣x∣>1|x| > 1∣x∣>1