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Infinite Series : Convergent Series of Nonnegative Terms

1. Show that if the infinite sum∑∞xn is a convergent series of non-negative terms, must ∑∞√nxn+1 be convergent? Prove or give a counterexample.

2. Find the value of ∑∞n=2 ln(1-1/n2).

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Solution Summary

A convergent series of nonnegative terms is investigated. The solution is detailed and well presented.