Alternating series

CALCULUS BC SERIES SERIES: PARTIAL SUMS: If (that it, the sequence of partial sums converges), then is the sum of the series so . In this case is CONVERGENT and has sum s. Thus a series converges if its sequence of partial sums converges. [Sec 11.2: p 2] EXAMPLES Does the series converge or diverge? 1. Partial sums: so, and thus the series converges and has sum = 1 2. Harmonic series: Partial sums: Thus the series diverges. [Sec 11.2: p3] 3. Here, (using partial fractions) Partial sum: Thus the series converges and has sum = 5. This is an example of a TELESCOPING SERIES.