Category: Relation and Functions

Question Number 29984 by abdo imad last updated on 14/Feb/18 $$provethat\sum _{n=1}^{\mathrm{\infty }}\frac{H_n}{n!}==e\sum _{n=1}^{\mathrm{\infty }}\frac{{\left(1\right)}^{\mathit{n}-1}}{\mathit{n}(\mathit{n}!)}.$$ Terms of Service Privacy Policy Contact:…

Question Number 29983 by abdo imad last updated on 14/Feb/18 $$findradiusandsumof\sum _{n=1}^{\mathrm{\infty }}\frac{n-1}{n!}{x}^n.$$ Commented by abdo imad last updated on 15/Feb/18 $${S}\left({x}\right)=\sum_{{n}=\mathrm{1}}…

Question Number 29978 by abdo imad last updated on 14/Feb/18 $$letgivex>0$$$$1)provethat{\int }_0^1\frac{dt}{1+t^x}=\sum _{n=0}^{\mathrm{\infty }}\frac{{(-1)}^n}{nx+1}$$$$\left.\mathrm{2}\right)\:{find}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}+\mathrm{1}}\:\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty}…

Question Number 29973 by abdo imad last updated on 14/Feb/18 $$find\sum _{n=1}^{\mathrm{\infty }}\frac{sin\left(n\alpha \right)}{n}{x}^{n}with-1<x<1.$$ Commented by abdo imad last updated on 16/Feb/18 $${let}\:{put}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{1}}…

Question Number 95465 by mathmax by abdo last updated on 25/May/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-{\mathrm{y}}^{{}^{\prime }}+2={\mathrm{x}}^2{\mathrm{e}}^{-\mathrm{x}}\mathrm{with}\mathrm{y}\left(0\right)=1\mathrm{and}{\mathrm{y}}^{{}^{\prime }}\left(0\right)=-1$$ Answered by mathmax by abdo last…