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# 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: *a _{n}* ≤ |

*a*|)

_{n}(c) Show that converges.