Convergence of Sequence Summation and Limit Prove

[l888l888l888]

Homework Statement

let (An) be a sequence in R with |summation from n=1 to infinity(An)|< infinity. Prove lim as n goes to infinity of ((A1 +2A2+...+nAn)/n) = 0

Homework Equations

The Attempt at a Solution

I think |summation from n=1 to infinity(An)|< infinity means the summation converges .I rewrote " lim as n goes to infinity of ((A1 +2A2+...+nAn)/n) = 0 " as "lim as n goes to infinity of ((summation from k=1 to n of nAn)/n)=0. Since I assmumed "summation from n=1 to infinity(An)" converges, that would imply the lim of An is 0. I don't know how to use this info to prove what i need to prove. Hope you can understand this. I don't know how to use tek.

 

[noc_njz]

Hint: If the summation of An converges and for all n ,Bn<An, then the summation of Bn converges.

 

[noc_njz]

Forgive my missing absolute. |Bn|<|An|