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.
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