converge or diverge, the sum as n goes from one to infinity of arcsin(1/n)

Correct, but what a complicated way !

As arcsin(1/n) > 1/n and the harmonic serie diverges, then this sum diverges, too (direct comparison test).

Correct, but what a complicated way !

As arcsin(1/n) > 1/n and the harmonic serie diverges, then this sum diverges, too (direct comparison test).