MA 114 Study Guide - Final Guide: Mathematical Induction, Binomial Series, Taylor Series
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Note that the point total on this exam is greater than 100 points, however no student will be given a grade of greater than 100. 100: find the limits of the following sequences. (a) lim n (b) lim n (c) lim n n2 + 1. 1 + 2n: suppose that a sequence a1, a2, . is de ned by an+1 = 4 . It can be shown that this sequence is bounded and increasing. Z e x2 dx (b) give the interval of convergence of the series you found in part a). (c) use the series in a) to express the de nite integral r 1/2 dx as a series. Determine how many terms are needed to approximate the integral to within 1/500 and evaluate a partial sum of the series, sn , which satis es e x2. 5. (a) state the integral test for convergence of a series. (b) what n is needed so that.
