Mark each statement True or False. Justify each answer. (a) The root test may show a series to be convergent when the ratio test fails. (b) The p-series Σ (1/n p ) converges iff p > 1. (c) If lim a n...

Mark each statement True or False. Justify each answer.

(a) The root test may show a series to be convergent when the ratio test fails.

(b) The p-series Σ (1/n^p) converges iff p > 1.

(c) If lim a_n
= 0, then Σ(−1)ⁿa_n
converges.

(d) The alternating harmonic series is conditionally convergent