Unformatted text preview: a n â‰¥ , s n = a 1 + Â·Â·Â· + a n , and Â± a n diverges. (a). Prove that âˆž âˆ‘ n =1 b n := âˆž âˆ‘ n =1 a n 1 + a n diverges . (d). What can be said about âˆž âˆ‘ n =1 c n := âˆž âˆ‘ n =1 a n 1 + na n and âˆž âˆ‘ n =1 d n := âˆž âˆ‘ n =1 a n 1 + n 2 a n ? #4. (12 points). Using twosided estimate 1 n + 1 < ln ( 1 + 1 n ) < 1 n , show that the sequence s n = 1 + 1 2 + 1 3 + Â·Â·Â· + 1 nln n, where ln x := log e x, is convergent....
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 Fall '09
 Math, Convergence, NC, 14 points, Dominated convergence theorem

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