HOMEWORK 6 - UCLA Mathematics
log2 X1 k=2 1 klogk does. This diverges by the previous problem, so P n 4 1=nlognloglogndiverges. (d)The terms of the series are positive and decreasing for n 2, and Z 1 2 logt t2 dt= logt t + Z 1 2 dt t2 = 1 + log2 2 is nite, so P (logn)=n2 converges. Alternatively, by the Cauchy condensation test, P n 2 (logn)=n 2 converges because X1 k=1 2k ................
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