Chapter 10.5, Problem 47E

Determine if the series Σ(-1)" 5n 1/2 + 3 converges 3n² - 3 n=1 absolutely, converges conditionally, or diverges, and justify your answer. The Series ✗(-1)" 5n / 2 +3 3n² - 3 n=1 converges by the since the absolute value of the terms Consider the absolute value of 5N 1/1 2 + 3 the series: 3n² - 3 n=1 by the to the p- series with p = which since a p-series will く if and only if n=1 5n³½ + 3 3m² - 3 and ☑ n=1 Since (−1)n 5n1/2 + 3 3n² - 3 Σ(-1)" n=1 5n 1/2 + 3 3n² - 3 > >

Give an example of an increasing sequence {an} that converges to 12. What can you conclude about the series En=1an? (Does it converge or diverge?) Give an example of a series that converges to 12. What can you conclude about the sequence {an}? (Does it converge or diverge?)

If the series >(-1)" a, is convergent and the seies an is convergent then n=1 we said the series2(-1)"a, is n=1 (a) conditionally convergent (b) absolutely convergent (c) None b d. e