# Convergence of series

#### Krizalid

##### Active member
Let $a_n$ and $b_n$ be sequences in $\mathbb R.$ Show that if $\displaystyle\sum b_n$ converges and $\displaystyle\sum|a_n-a_{n+1}|<\infty,$ then $\displaystyle\sum a_nb_n$ converges.