Question

Find a series ∑a_n for which ∑(a_n)^2 converges but ∑|a_n| diverges

Answer 1

Consider
1 - 1/2 + 1/3 - 1/4 + ... (alternating harmonic series)


1 + 1/4 + 1/9 + 1/16 + ... = π²/6


1 + 1/2 + 1/3 + 1/4 + ... diverges (harmonic series)

Answer 2

thanks!!