Consider the Power Series $\sum _ { k = 1 } ^ { \infty } \frac { ( - 1 ) ^ { k } } { k } x ^ { k }$

Essay

Consider the power series $\sum _ { k = 1 } ^ { \infty } \frac { ( - 1 ) ^ { k } } { k } x ^ { k }$ .(a) Find the radius of convergence.(b) Determine what happens at the end points (absolute or conditional convergence, or divergence).