Category: Relation and Functions

Question Number 60504 by prof Abdo imad last updated on 21/May/19 $$let{S}_n=\sum _{k=1}^n\frac{1^2+2^2+\dots k^2}{1^4+2^4+\dots +k^4}$$$$studytheconvergenceof{S}_n$$…

Question Number 60499 by abdo mathsup 649 cc last updated on 21/May/19 $$findthevalueof\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^3{(n+1)}^4}$$ Commented by maxmathsup by imad…

Question Number 125968 by bramlexs22 last updated on 16/Dec/20 $$Findf\left(x\right)suchthat$$$$f\left(x\right)+f\left(\frac{1}{1-x}\right)=x$$ Answered by liberty last updated on 16/Dec/20 $$\left(1\right)f\left(x\right)+f\left(\frac{1}{1-x}\right)=x$$$${replace}\:{x}\rightarrow\frac{\mathrm{1}}{\mathrm{1}−{x}}\: \…

Question Number 60203 by meme last updated on 18/May/19 $$demonstrate$$$$\mid sin\left(y\right)-sin\left(x\right)\mid ⩽\mid y-x\mid$$ Commented by Mr X pcx last updated on 19/May/19 $${let}\:{f}\left({x}\right)={sinx}\:{we}\:{have}\:{f}^{,} \left({x}\right)={cosx}…

Question Number 60197 by Mr X pcx last updated on 18/May/19 $$valculste{lim}_{n\to +\mathrm{\infty }}(ln\left({\left(\prod _{k=1}^n(1+\frac{k^3}{n^3})\right)}^{\frac{1}{n}}\right)$$ Commented by Mr X pcx…