The question is: estimate the sum, from 2 to infinity, of 1 / (n^2 + 4) to within 0.1 of exact value. I have the following: the integral from n to inf. of 1 / (x^2 + 4) is (pi/4 - 1/2 arctan(n/2)). Next, in order to find the number of partial sums to use, set Sn + the integral from n+1 to infinity < S < Sn + the integral from n to infinity. This gives (pi/4 - 1/2 arctan[(n+1)/2]) < (remainder) < (pi/4 - 1/2 arctan(n/2)). I can only assume from here that you are meant to subtract the lesser from the greater and set (1/2 arctan[(n+1)/2]) - 1/2 arctan(n/2) < 0.2. So arctan((n+1)/2) - arctan(n/2) < 0.4. What?