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Motivation: It's known that there is a constant $0On sums involving Euler's totient function

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 $\lim a_n=0$.

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    How far did you get?2012-04-05

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