1. The problem statement, all variables and given/known data Determine whether the series Ʃ(1 to infinity) sinx / x converges or diverges. 2. Relevant equations This question appears in the integral test section, but as far as i know the integral test can only be used for decreasing functions, right? 3. The attempt at a solution Using the ratio test, limx->infinity sin(x+1)/(x+1)*(sinx/x)=limx->infinity x*sin(x+1)/((x+1)(sinx)) This is where i got stuck-this limit oscillates between positive infinity and negative infinity. Using the root test, i need to find the limit of (sinx)^(1/x) as x approaches infinity, which also gets me nowhere. we have not done taylor series yet so i'm sure there is a relatively simple approach to this question...please help?