1. The problem statement, all variables and given/known data "For the given series, write formulas for the sequences an , Sn, Rn and find the limit as n->∞ (if it exists) 2. Relevant equations ∑∞1 ((1/n) - 1/(n+1) 3. The attempt at a solution I know how to take the limit, that's no problem. I'm a bit confused about what an , Sn, Rn are referring to. Maybe I'm just misunderstanding the usage... My book speaks generally of defining them (by that i mean, no formal definition is given but it often refers to a previous example) however it does say this: Let us call the terms of the series a so that the series is "a1 + a2 + a3 + a4 + · · · + ann + · · · ." Remember that the three dots mean that there is never a last term; the series goes on without end. Now consider the sums Sn that we obtain by adding more and more terms of the series. We define S1 = a1, S2 = a1 + a2, S3 = a1 + a2 + a3, · · · Sn = a1 + a2 + a3 + · · · + an It then goes further to say: The difference Rn = S − Sn is called the remainder (or the remainder after n terms). From (4.6), we see that.... Where S is the lim n-> ∞. So can Rn not be found if there's no limit? Also, why even write down an if it's just the same as Sn?