# Math Help - prove this convergence

1. ## prove this convergence

suppose that:

sigma ( An ) converges and An >0
Show that there exist Bn with Bn/An tends to 0 and Sigma( Bn) converges

2. Originally Posted by szpengchao
suppose that:

sigma ( An ) converges and An >0
Show that there exist Bn with Bn/An tends to 0 and Sigma( Bn) converges
If $\sum_{n=0}^{\infty}a_n$ converges then it absolutely converges, which means $\sum_{n=0}^{\infty}a_n^2$ will converge. Take $b_n = a_n^2$.