Suppose that {an} is a non- negative sequence satisfying \(\rm \sum_{n=1}^{\infty} a_n=\infty\) then the series
\(\rm \displaystyle\sum_{n=1}^{\infty} \frac{a_n}{\left(a_1+a_2+\cdots+a_n\right)^k}\) is
1
Convergent if k > 1
2
Convergent if k ≥ 1
3
divergent if 0 < k ≤ 1
4
divergent if 0 < k < 1