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???