Let $ a_1,a_2,a_3,...a_n $ be a set of positive integers. Does there exist any closed form for the approximation of the sum $$ \sum_{i=p}^n\operatorname{floor}\left(\frac{a_p}{i-p+1}\right) ?$$

If not so, can we atleast get a recursive relation between $ sum(p) $ and $ sum(p-1) $? Call $$ sum(p) = \sum_{i=p}^n\operatorname{floor}\left(\frac{a_p}{i-p+1}\right) $$

The relation should be like if I have the value of $sum(p)$ and I know what $a_{p-1}$ is, I can get the value of $sum(p-1)$. Can we get a recursive relation like this?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.