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Series

Series

Absolute Convergence vs. Conditional Convergence Exercises

Example 1

Determine whether the series converges conditionally, absolutely, or not at all.

Example 2

Determine whether the series converges conditionally, absolutely, or not at all.

Example 3

Determine whether the series converges conditionally, absolutely, or not at all.

Example 4

Write a real proof that absolute convergence implies convergence.

Assume that  converges.

(a) Show that  converges.

(b) Show that  converges. (hint: an ≤ |an|)

(c) Show that  converges.