1. The problem statement, all variables and given/known data If you sum this from one to infinity. Ʃ (cos(1/(n)^2 - cos(1/(n+1)^2) 2. Relevant equations 3. The attempt at a solution Ʃ (cos(1/(n-1)^2 - cos(1/(n+1)^2) This is telescoping if you work that out for the partial nth partial sum you get cos(1) - cos(1/(n+1)^2) if you take the limit you get cos(1) -1 which is negative. If you punch it in on wolfram you get the same thing. Can the partial sum be negative ?