Question Number 35603 by abdo mathsup 649 cc last updated on 20/May/18
![let x ∈ R and {x}=x −[x] prove that ∫_1 ^(+∞) (({x})/x^2 ) dx is convergent and find its value .](https://www.tinkutara.com/question/Q35603.png)
$${let}\:{x}\:\in\:{R}\:\:{and}\:\left\{{x}\right\}={x}\:−\left[{x}\right] \\ $$$${prove}\:{that}\:\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\left\{{x}\right\}}{{x}^{\mathrm{2}} }\:{dx}\:{is}\:{convergent}\:{and}\:{find} \\ $$$${its}\:{value}\:. \\ $$