9.5_LA-Solutions-Ratio_Test_and_Convergence_Tests

# 9.5_LA-Solutions-Ratio_Test_and_Convergence_Tests - D^ Z d...

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

MthSc 108-9.5 (Ratio Test & Convergence Tests) Solutions 1. Apply the Ratio Test to the series 1 n 3 n = 1 . What is your conclusion about the convergence/divergence about this series based on your results of the Ratio Test? What other test might you use? Observe that the terms of the series are positive and that the ratio test can be applied. Compare this series to the convergent p-series (p=3>1), 1 n 3 n = 1 . lim n →∞ a n + 1 a n = lim n →∞ 1 ( n + 1) 3 1 n 3 = lim n →∞ n 3 ( n + 1) 3 = 1 Since ρ = 1, the Ratio Test applied to this series is inconclusive. However, it is easy to see that 1 n 3 n = 1 is a convergent p-series where p = 3 > 1 . 2. Use the Limit Comparison Test to determine if the series 1 2 n 2 + n n = 1 converges or diverges. Compare this series to the convergent p-series, 1 n 2 n = 1 , where p = 2 > 1 . lim n →∞ a n b n = lim n →∞ 1 n 2 1 2 n 2 + n = lim n →∞ 2 n 2 + n 1 1 n 2 == lim n →∞ 2 + 1 n

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 01/30/2011 for the course MTHSC 108 taught by Professor Any during the Spring '08 term at Clemson.

### Page1 / 3

9.5_LA-Solutions-Ratio_Test_and_Convergence_Tests - D^ Z d...

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

View Full Document
Ask a homework question - tutors are online