Explore BrainMass
Share

Limits, convergence and divergence

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

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)?

© BrainMass Inc. brainmass.com December 20, 2018, 6:15 am ad1c9bdddf
https://brainmass.com/math/real-analysis/limits-convergence-and-divergence-361052

Solution Summary

Limits, convergence and divergence are exemplified.

$2.19