Consider the alternating series A= _ n=1 ^ (-1)^ n
MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Consider the alternating series
A=n=1∑∞(−1)nn2+1n.
Answer the following questions fully.
(a) Write the series formed by taking the absolute value of each term of A.
(b) Compare the absolute-value series from part (a) to a suitable benchmark series and determine whether it converges or diverges. Show all inequalities and indicate any value N beyond which they hold.
(c) Using your result from part (b), classify the convergence of A as absolute, conditional, or neither. Provide full justification, including any additional tests needed for the alternating nature of A.