222 theorem lim a 0 a iftheseriesisconvergentthen n

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Unformatted text preview: ms must have a limit of 0. Example an n n 1 n 1 n n 1 lim an is convergent. a is divergent. n Example an 1 n 1 0 n n lim an a n is convergent. ??? Not necessarily convergent. Stay tuned for the answer. Divergence Test an lim an 0 If , then the series, , is divergent. n n 1 (This test is a consequence of the theorem.) Limit Laws If and are convergent, and and a b a a a b b b , then , , and are can a b convergent, and n n n n n i) ca ca ii) a b a b iii) b a b a n n n n n n n n Summary an lim an L If , and L is finite, then is convergent. n lim an 0 If ,then is divergent. an n A geometric series is convergent if the magnitude of the common ratio is less than 1. s a 1 r If a geometric series is convergent, the sum is , where r is the common ratio and a is the first term....
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This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.

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