Motivation: It's known that there is a constant $0
My intention is to generalize this result.
So my question is: Suppose that $\{a_n\}_{n=1}^{\infty}$ is a non-increasing sequence of positive reals, is there a constant $0 Remark: if $\lim a_n>0$, then we can simply take $K=\frac{K'\lim a_n}{a_1}$ where $K'$ is the constant appearing in the first result stated above, so the problem is really when $\lim a_n=0$.