No idea how to do this one. I know that if ($b_n$) is convergent it's bounded and either increasing or decreasing, hence ($a_n$) is going to converge but I have no idea how to prove that or find the limit.
Given two sequences of positive real numbers ($a_n$), ($b_n$) such that n belongs to the naturals. ($b_n$) is convergent and ($a_1 + a_2 + ... + a_n$) is less than or equal to $b_n$ for every positive integer $n$. Prove that ($a_n$) must converge and what is its limit?