242hw7solns

# 242hw7solns - Math 242 Homework 7 Solutions In questions 1...

This preview shows pages 1–2. Sign up to view the full content.

Solutions In questions 1 through 8, determine whether the series converges or diverges. (Give reasons.) 1. X n =1 1 2 n Solution. This series is 1 2 times the harmonic series, so it diverges . 2. X n =1 ln ± n 2 + 1 2 n 2 + 1 ² Solution. Note that when n → ∞ , we have n 2 + 1 2 n 2 + 1 1 2 . Therefore the terms of this series approach ln ± 1 2 ² , which is not 0. Therefore, by the “Pre-Test” (or “Test for Divergence”), the series diverges . 3. X n =1 1 + 3 n 2 n Solution. This series is the sum of the two series X n =1 1 2 n and X n =1 3 n 2 n = X n =1 ± 3 2 ² n . The second of these is a geometric series with r = 3 2 , so it diverges. Therefore the original series diverges . 4. X n =1 n e n Solution A. We can say n < 2 n . Therefore n e n < 2 n e n = ± 2 e ² n . But X ± 2 e ² n is a geometric series with r = 2 e < 1, which converges. Therefore by basic comparison, the original series converges . 1

This preview has intentionally blurred sections. Sign up to view the full version.

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

## This note was uploaded on 12/07/2011 for the course MATH 242 taught by Professor Wang during the Spring '08 term at University of Delaware.

### Page1 / 4

242hw7solns - Math 242 Homework 7 Solutions In questions 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online