Calculus II (MAT 146) Dr. Day Monday, April 9, 2018 Series Worth Remembering (11.2) Your First Tests For Convergence! (11.2, 11.3) The Divergence Test (11.2) The Integral Test (11.3) The p-Series Test (11.3) Monday, April 9, 2018 MAT 146

Fact or Fiction? (1) If the series 𝑛=1 ∞ 𝑎 𝑛 is convergent, then lim 𝑛→∞ 𝑎 𝑛 =0.   (2) If lim 𝑛→∞ 𝑎 𝑛 =0, then the series 𝑛=1 ∞ 𝑎 𝑛 is convergent. (3) If lim 𝑛→∞ 𝑎 𝑛 does not exist or if lim 𝑛→∞ 𝑎 𝑛 ≠0, then the series 𝑛=1 ∞ 𝑎 𝑛 is divergent. Monday, April 9, 2018 MAT 146

Notable Series A geometric series is created from a sequence whose successive terms have a common ratio. When will a geometric series converge? Monday, April 9, 2018 MAT 146

Notable Series The harmonic series is the sum of all possible unit fractions. Monday, April 9, 2018 MAT 146

Notable Series A telescoping sum can be compressed into just a few terms. Monday, April 9, 2018 MAT 146

Our first Series Convergence Test Our first Series Convergence Test . . . The nth-Term Test also called The Divergence Test If lim 𝑛→∞ 𝑎 𝑛 does not exist or if lim 𝑛→∞ 𝑎 𝑛 ≠0, then the series 𝑛=1 ∞ 𝑎 𝑛 is divergent.   Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146

Monday, April 9, 2018 MAT 146