Which of the following series are conditionally convergent? Why

i) Σ (-e)^-n

ii) Σ (-1)^n * 1/n

iii) Σ (-1)^n * 1/n^2

I understand that in order for conditional convergence you must have a series such that Σ | an | is divergent while Σ an is convergent. Just trying to check my work for these problems.

Only ii is conditionally convergent. If you take absolute values of the terms in that series, you get the divergent harmonic series.

The first one is geometric with |r| = |1/e| < 1. The last one has absolute value terms Σ 1/n² which is a convergent p-series.