1. The problem statement, all variables and given/known data The series, 1 / (1 x 2) + 1 / (2 x 3) + 1 / (3 x 4) + ... + 1 / [n(n + 1)] + ... is not a geometric series. (A) Use the identity 1 / [k(k + 1)] = 1 / k - 1 / (k + 1) to find an expression for the nth partial sum Sn and (B) use it to find the sum of the series. (C) Also, how many terms of the series would be required so that the partial sum differs from the total sum by less than 0.001? 2. Relevant equations 1 / [k(k + 1)] = 1 / k - 1 / (k + 1) 3. The attempt at a solution (A) I do not understand how the provided identity could be used to find Sn. However that I think that the following is true, Sn = 1 / (1 x 2) + 1 / (2 x 3) + ... + 1 / [n(n + 1)] I cannot seem to make an expression such as the answer, 1 - 1 / (n +1). (B) I understand that the limit of Sn as n approaches infinite is equal to the sum of the series, but, alas, I do not have an expression for Sn. (The answer is 1.) (C) From my incomplete understanding of infinite series, I would think that the partial sum Sn would have a difference of less than 0.001 with the total sum L (the limit of the infinite series), or, Sn - L < 0.001 Sn < 0.001 + L Here, I would think there would be manipulation of Sn to isolate n for this inequality. (The answer is 1000.) ---- Much appreciation for any help! This is my first time in maybe 3 years since doing any form of obvious sequences and series, so the smallest of corrections (incorrect terminology) is completely welcomed.