Chapter 10.1, Problem 10E

2. Alternating series: a. Consider the series 4 – + -+ 4 - · · . This is a convergent series by the alternating series test. Using an appropriate error estimate, determine the partial sum that will approximate the infinite sum with error less than 0.0001. (-1)* 2 (2k+1)3k-0.5 · b. Another series that converges to the exact same value as the series in part (a) is > -o Using an appropriate error estimate, determine the partial sum that will approximate the infinite sum with error less than 0.0001. C. Choose either of the above two series and approximate it with error less than 0.0001. What famous number do these two converge to?

Number 31

(- 1)7+(n+2) n(n+ 1) 1. Determine if the series converges absolutely, converges conditionally, or diverges. You may use any test(s) learned so far in the course. n=1

Determine the sum of the series. (-1)n-¹n n³ + 5 n=1 Type a simplified fraction if convergent, otherwise type DIVERGENT in uppercase letters.