Barrons AP Calculus

Example 28 __

Determine whether converges absolutely, converges conditionally, or
diverges.

SOLUTION: We see that , not 0, so by the nth Term Test the series

    is  divergent.

BC  ONLY

Example 29 __

Determine whether converges absolutely, converges conditionally, or

diverges.

SOLUTION: Note that, since ; the series passes the nth Term

Test.

Also,       for all n.

But is the general term of a convergent p-series (p = 2), so by the Comparison
Test the nonnegative series converges, and therefore the alternating series
converges absolutely.

Example 30 __

Determine whether converges absolutely, converges conditionally, or
diverges.

SOLUTION: is a p-series with , so the nonnegative series diverges.

We see that and , so the alternating series converges;
hence is conditionally convergent.

APPROXIMATING THE LIMIT OF AN ALTERNATING

SERIES