(a) Starting with the geometric series ∑[infinity]n=0 xn, find the sum of the series ∑[infinity] n=1 (b) Find the sum of each series: (c) Find the sum of each series. nxn−1, ∑[infinity] (i) |x| < 1. nxn, |x| < 1 ∑[infinity] n (ii) 2n n=1 ∑[infinity] n=2 ∑[infinity] n 2 − n 2n n=1 (iii) ∑[infinity] n 2 2n n=1 n=2'

Nina has prepared the following two-column proof below. she is given that ∠oln ≅ ∠lno and she is trying to prove that ol ≅ on. triangle oln, where angle oln is congruent to angle lno step statement reason 1 ∠oln ≅ ∠lno given 2 draw oe as a perpendicular bisector to ln by construction 3 ∠leo ≅ ∠neo transitive property of equality 4 m∠leo = 90° definition of a perpendicular bisector 5 m∠neo = 90° definition of a perpendicular bisector 6 le ≅ en definition of a perpendicular bisector 7 δole ≅ δone side-angle-side (sas) postulate 8 ol ≅ on cpctc nina made two errors in the proof. identify and correct the errors.