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Limits, convergence and divergence

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Suppose a_n is strictly greater than zero
a. Show that lim( as n goes to infinity) a_n/(a_n+1) =0 if and only if lim (as n goes to infinity) a_n=0

b, Prove that sum (n = 1 to infinity) a_n diverges if and only if
sum(n=1 to infinity) a_n/(a_n+1) diverges.

c. What can be said about (convergence or divergence) of
sum(n=1 to infinity) a_n/(n^2 a_n+1)?

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Solution Summary

Limits, convergence and divergence are exemplified.