LEARNING GOALS: to use the corollary to the Alternating Series Test to find an upper bound on the error in

approximating the sum of a convergent alternating series by its Nth partial sum; to use the Alternating Series Test to

show a given series converges by verifying the non-alternating part of the general term of the series is positive, decreasing,

and has a zero limit.

2. In Question 1(a), we showed

n=0

(-1)"

3n+ 1

converged by the Alternating Series Test. Use this fact to find an upper

(−1)n+1 1 1

3n+1

bound on the error associated with the approximation

n=1

4 7

+

1

10

1

13

Justify your answer.