8. (Optional. Bonus +2 points if you answer it correctly) Much like a geometric series, an arithmetic series is a series _ ax in which each term is computed from the previous one by adding (or subtracting) *=1 a constant r. More precisely, > ax is an arithmetic series if there's a constant r such that akti = ak tr k=1 for all k (or r = ak+1 - ak). (a) Write out the first four terms of the series (that is, a1, a2, a3, and a4) in terms of a1, and r. n (b) Write out the nth partial sum Sn = _ ax in . .. notation in terms of a1, n and r only. k=1 n (c) Knowing that Ck = 1+2+ ... +n = "("+, find a closed formula for the nth partial sum k=1 n Sn = E k=1