Let u = (xi. ... xn ) and v = {y1, Y n ) be elements of en. Prove that (u, v) = X1Y1 + + X n Y n satisfies the inner product axioms for a complex vector space.

Fall 2011 MA 16200 Study Guide - Exam # 3 (1) Sequences; limits of sequences; Limit Laws for Sequences; Squeeze Theorem; monotone sequences; bounded sequences; Monotone Sequence Theorem. ∑1 ∑n ∑ (2) In▯nite seriesan; sequence of partial nums s ak; the seriesanconverges to snif s → s. n=1 k=1 n=1 (3) Special Series: 1 ∑ n▯1 2 3 a (a) Geometric Series: ar = a(1 + r + r + r + ···)1 − r, if |r| < 1 (converges). n=1