Let R denote the radius of convergence of power series \(\rm \displaystyle \sum_{k=1}^{\infty} k x^{k}\). Then
1
R > 0 and the series is convergent on [- R, R]
2
R > 0 and the series converges at x = -R but does not converges at x = R
3
R > 0 and the series does not converge outside (-R, R)
4
R = 0