# Leibniz and convergence?

1. Apr 16, 2009

### Dell

in the following question i am given the series:

Σ((-1)^(n-1))*1/(n+100sin(n))

and am asked if the series converges or diverges.

as far as i know Leibniz's law for series with alternating signs states that if the series of the absolute values diverges then we check the following 2 conditions for convergence:
#1) lim(n->infinity) An =0
#2) An > A(n+1)

i have managed to prove that the absolute series diverges so now i need to check the 2 conditions,

#1) lim(n->infinity) An =0 can easily be proven so i move onto the next condition

#2) An > A(n+1)
since An is dependant on sin(n), how can i say for sure which is larger? since sin(n) can vary from -1 to 1, does this not mean that the series diverges??

in my book it says that the series converges, is this a misprint on their behalf or am i missing something here???