MAT 21C Study Guide - Midterm Guide: Squeeze Theorem, Ibm System P, Integral Test For Convergence
52
MAT 21C Full Course Notes
Verified Note
52 documents
Document Summary
Determine whether or not the following series converges, and if so, nd the sum: For each of the following series, determine whether it converges or diverges: X n=2 (c) n (n2 1)3/2 . Determine whether or not the following sequence converges, and if so, to what: Solution: for all n 1, we have. 2n 1 so [by the sandwich theorem] limn sin n. Using only the denitions of convergence for series and for sequences, de- termine whether or not the following series converges, and if so, to what: 1 n(n+1) = 1 n 1 n+1 n(n + 1) n=1. Solution: using the hint, the partial sum sn is given by sn = Given any > 0, if n > 1. , and if n > n , then n > 1. By the denition of sequence convergence, we see that limn sn = 1. By the denition of series convergence, we see thatp .
