<p>Not sure if this is the appropriate forum but whatever.</p>
<p>Does any math person know if (-1)^n/n as n goes to infinity converges or diverge?</p>
<p>I would think that it would converge since any number divided by infinity is 0.</p>
<p>Is this a sequence or a series? It converges in both cases, but the reason is different for the two. Notice that the absolute value of each term is just 1/n. 1/n is a convergent sequence (for the reason you gave), but as a series (it’s known as the harmonic series) it doesn’t converge. (-1)^n/n does converge as a series because it alternates positive and negative and because the sequence of terms converges to 0 (any alternating series with terms whose absolute values shrink and go to 0 are convergent).</p>
<p>Physics Forums is a good site for this type of question.</p>