Section10.3a-ConvergenceOfSeriesWithPositiveTerms

1 1 dx x2 an 1 n2 convergessoconverges n 1 a3 a2 1 n2

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: converges, 1 then so does the series. 1 1 dx x2 an 1 n2 converges, so converges. n 1 a3 a2 1 n2 a4 … n What’s the Difference? 1 n2 decreases faster than an 1 n2 1 n an 1 n Example 1 For what values of p does the series, , n converge? n 1 1 1 dx xp 1 xp is continuous, positive, and decreasing, if p>0. The integral converges if p>1. Diverges otherwise. Therefore, 1 np n 1 Converges for p>1 by Integral Test. Diverges for 0 < p ≤ 1 by Integral Test. Diverges for p ≤ 0 by Test for Divergence. p P‐ Series Test 1 np n 1 Converges for p > 1. Diverges otherwise. Note As with all series, convergence depends only on behavior of the “tail”. Examples Determine if the following series converge or diverge. 1 n4 n 3 1 n 4 n 1 n 1 1 n 1 4 Try It Show whether the following series converge or diverge. Pay careful attention to notation. Justify all steps. ne n n 1 1 n ln n n 2 en n 1 3n n2 n2 5 1 n2 5...
View Full Document

This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.

Ask a homework question - tutors are online