Category: Relation and Functions

Question Number 63165 by mathmax by abdo last updated on 29/Jun/19 $$let{W}_n=\sum _{k=0}^n\frac{1}{3k+1}determine{W}_{n}intermsof{H}_n$$$$H_n=\sum _{k=1}^n\frac{1}{k}$$ Terms of…

Question Number 63101 by mathmax by abdo last updated on 29/Jun/19 $$calculateS=\frac{1}{1\times 2}+\frac{1}{3\times 4}+\frac{1}{5\times 6}+\dots ..$$ Commented by mathmax by abdo last updated on 29/Jun/19 $${let}\:{try}\:{another}\:{way}\:{we}\:{have}\:\frac{{d}}{{dx}}{ln}\left(\mathrm{1}+{x}\right)\:=\frac{\mathrm{1}}{\mathrm{1}+{x}}\:=\sum_{{n}=\mathrm{0}} ^{\infty}…

Question Number 62962 by fyyac c last updated on 27/Jun/19 $$P\left(x\right)={\tan }^{-1}\left(x\right)=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^n{x}^{2n+1}}{2n+1}$$$$P_{1000}\left(x\right)=?whatisthissumintermsofx?$$ Terms of Service Privacy…

Question Number 128496 by mathmax by abdo last updated on 07/Jan/21 $$\mathrm{calculate}\mathrm{A}=\frac{1}{{(2-\sqrt{6})}^4}+\frac{1}{{(2+\sqrt{6})}^4}$$ Commented by liberty last updated on 08/Jan/21 $$\frac{\left(\mathrm{2}−\sqrt{\mathrm{6}}\right)^{\mathrm{4}} +\left(\mathrm{2}+\sqrt{\mathrm{6}}\right)^{\mathrm{4}}…

Question Number 128425 by bramlexs22 last updated on 07/Jan/21 $$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\tan \mathrm{x}\mathrm{and}\mathrm{f}\mathrm{is}\mathrm{inverse}$$$$\mathrm{of}\mathrm{g},\mathrm{then}{\mathrm{g}}^{\prime }\left(\mathrm{x}\right)\mathrm{is}\mathrm{equal}\mathrm{to}$$$$\left(\mathrm{a}\right)\frac{1}{1+{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}\left(\mathrm{b}\right)\frac{1}{1-{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}$$$$\left(\mathrm{c}\right)\frac{1}{2+{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}\left(\mathrm{d}\right)\frac{1}{2-{(\mathrm{g}\left(\mathrm{x}\right)-\mathrm{x})}^2}$$ Answered by liberty…