(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'

Match the following reasons with the statements given to create the proof. 1. do = ob, ao = oc sas 2. doc = aob given 3. triangle cod congruent to triangle aob vertical angles are equal. 4. 1 = 2, ab = dc if two sides = and ||, then a parallelogram. 5. ab||dc if alternate interior angles =, then lines parallel. 6. abcd is a parallelogram cpcte