Telescoping Series & P-Series Objectives: Be able to describe the convergence or divergence of p-series and telescoping series. TS: Explicitly assess information and draw conclusions Warm Up: Find the sum of each infinite series. 1) 2)

P-Series The p-series is (any of) the series for any positive real number p. The series is always convergent if p > 1. For all other values of p it is divergent. For example:

Examples: Describe whether or not the series diverges or converges.

Telescoping Series A telescoping series is any series where nearly every term cancels with a preceding or following term. For instance, the series

Example: