1. Assume an > 0, bn > 0. and bn converges. Show that if lim an/bn = 0, then an an converges.
Solution
(summation of an) < (summation of an/bn )*(summation of bn) for n-->infinity
given an/bn =0 as n--> infinity so summation of an/bn as n-->infinity converges and also given
summation of bn converges so RHS converges LHS < RHS so LHS converges so (summation
of an) as n--> infinity converges