Homework 3 Solutions - Stanford University
n are geometric series with r= 1, and hence diverge by Theorem 22.4. However, a n+ b n= 0 for all nso the n-th partial sum of P 1 n=1 (a n+ b n) is zero for all n, giving P 1 n=1 (a n+ b n) = 0 converges. 24.9. Prove that if fa ngis a decreasing sequence of positive numbers and P 1 n=1 a n converges, then lim n!1na n= 0. Deduce that P 1 n=1 1 s ...
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