Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

given a sum in the form $ \sum_{1\le x \le n} [ f(x)] =S $ , here $ [ x]$ is the floor function which takes only integer values.

how could i evaluate or give a good estimation ??

i know that the sum $ \sum_{1\le x \le n} f(x) - [ f(x)] $ would be less or equal than $ n-1 $ but what a better estimation can be done ?

could i expand $ [ f(x)] $ into a fourier series on the interval $ (1,n) $ to make it easier to evalute the series ?

wher could i find more references :D ?? thanks.

share|improve this question
    
Do you have a particular $f$? –  Berci Sep 28 '12 at 16:16
    
no, let us assume $ f(x) $ is smooth enough –  Jose Garcia Sep 28 '12 at 16:18
1  
If $f$ is the smooth function $0$, then the error is $0$. If $f$ is the smooth function $1-\varepsilon$, your error is arbitrarily close to $n$. –  Hagen von Eitzen Sep 28 '12 at 16:21
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.