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More - Math 21C Kouba More Sequences and Series 1 Consider...

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Unformatted text preview: Math 21C Kouba More Sequences and Series 1.) Consider the sequence given by (11 = 3 and an+1 : n: Ian for n = 1, 2,3, . .. . Does 00 the series Z(—1)nan converge or diverge ? n=1 . . 3aln+1 2.) Con51der the sequence given by a1 = 3, a2 = 1, and an” 2 an + 1 for n 2 1, 2,3, . .. . m 1 Does the series 2 (a )n converge or diverge ? n=1 n 3.) a.) For What values of n, if any, is n2 < (ln n)l“" ? 00 1 b.) Does the series 2 ( converge or diverge ? n22 in n) 1n n n—)oo n k 4.) Let 3,, = E ln (k: + 1). Evaluate lim (ln(3n) + 3n). k=1 n l 5.) Consider the sequence given by an 2 671:. for n = 1, 2, 3, . . . . a.) Show that an+1 > an for all values of n. b.) What, if anything, can be said about 11111 an ? 71—)00 6.) Use any test to determine the convergence or divergence of each series. w 1 m 1 w 1 ” _,, @n—nn 3..) 2:1"; b) 21 711/71 C.) 22% d.) 2—277] 8111 [—7—] 0° lnn 0° Inn 00 (2.71)“n! 0° enn! __ , _ , ————— h. _ 0° 1 0° (Inn)4 0° (51n(1/n))4 . k. ‘) swannr “ Z Z; n ...
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