Math 222 Lecture 1 - Sequences and Series, Study notes of Analytical Geometry and Calculus

Download Math 222 Lecture 1 - Sequences and Series and more Study notes Analytical Geometry and Calculus in PDF only on Docsity! Worksheet 14 Math 222 – Lecture 1 – Section 315 (WES) Friday, Oct. 10, 2008 Happy Friday! 1. Complete the following definitions: A sequence is... A series is... The sequence {an} has limit L if and only if... The series ∑∞ n=1 an converges to the sum L if ... 2. For each of the following, • write the series in the form ∑β n=α an, • calculate the nth partial sum (break into cases if need be), and • state whether the series converges or not. If it does, what does it converge to? (a) 1 + 1 + 1 + · · ·+ 1︸ ︷︷ ︸ 15 (b) 1 + 1 + 1 + · · · (c) 1− 1 + 1− 1 + · · · (d) 1 + 12 + 1 4 + 1 8 (e) 1 + 12 + 1 4 + 1 8 + · · · (f) 12 + 1 3 + 1 4 + 1 5 · · · (g) 1− 12 + 1 2 − 1 3 + 1 3 − 1 4 + 1 4 − · · · (h) 12 + 1 3 + 1 4 + 1 5 · · · (i) 1 + e+ e2 + e3 + · · · (j) 1 + e−1 + e−2 + e−3 + · · · 1