Ratio Test, Conditional Convergence, divergence, and interval of convergence

Question

How do I find the values that x conditionally converges, diverges, and the interval of convergence?

the power series is the sum from n=1 to infinity of (-1)^(n+1)((x^n)/n)

Part a: i did the ratio test and got x<1

part b: asks for the values of x that the series conditionally converges

part c: asks for the values of c that the series diverges

part d: asks for the interval of convergence

Answer 1

Convergence: Correct about ratio test. Doesn't converge for +/- 1 (harmonic series) |x|<1

Conditional Convergence: xⁿ⁺¹/(n+1) < xⁿ/n for all n. or x (n/n+1) 1. Or x ≤ 1 but note that -1 doesn't work (harmonic series again), but 1 does. So same range as first part, but x = 1 added