MATH 2414 Lecture Notes - Lecture 14: Ibm System P, Conditional Convergence, Ratio Test
5 Oct 2018
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A series 2an is absolutely convergent if elan1 is convergent. If a series is absolutely convergent then it is convergent. If conditionally convergent is convergent but not absolutelyconvergent then it is a series n c1 ht e l l t l. I 1c l 11 tc it1 c it1 t. Determinewhether the series is absolutelyconvergent conditionally convergent or divergent. Ie th convergentby p series as c15e n absolutely convergent n os c yn11. I tbh"t as cdntl sn h bn ht decreasingbecause nun constant tdenon increasing in divergentby p series. I jiffsbn n"ismsth o ty converges byalternating seriestest conditionallyconvergent. For a series ni an: if nlismos aami. If lisa aahn: if nlims i an i. L s 1 then the series is absolutelyconvergent. 1 then this test is in conclusive then the series diverges or as hints la i l for large enough. I 3t ztn things cnn. tl zlnismscltth 3 multiplybyreciprocal i.
