4. (a) Mimicking how integrals work, you can always "pull" constant factors outside a series: _ can = c Can. Compute > 17 n n+] n=2 (b) However, you must be careful splitting sums (or differences) inside series like you would for an integral: [(On on) = Ean + Ebn does not always hold (for example, _(1 - 1) / 1 - 1, since LHS is 0, but the RHS diverges). But if you can argue that both _ on and _ b, converge, then it's legal: E(an th,) = Canton, if both >an, > by converge. Compute the sum of the following series: + arctan n - arctan(n - 1) ). n=1