Category: Relation and Functions

Question Number 31422 by abdo imad last updated on 08/Mar/18 $$find\sum _{n=1}^{\mathrm{\infty }}arctan\left(\frac{2}{16n^2+8n-2}\right).$$ Commented by rahul 19 last updated on 08/Mar/18 $${can}\:{u}\:{plz}\:{provide}\:{sol}.\:{for}\:{this}\:{one}\:.…

Question Number 31417 by abdo imad last updated on 08/Mar/18 $$letgive{u}_n=\sum _{k=1}^n\frac{1}{k}-ln\left(n\right)$$$$1)provethat{u}_{n}isconvergent$$$$2)if\gamma ={lim}_{n\to \mathrm{\infty }}{u}_{n}provethe0<\gamma <1.$$ Terms of…

Question Number 96836 by mathmax by abdo last updated on 05/Jun/20 $${\mathrm{a}}_{\mathrm{n}}\mathrm{is}\mathrm{a}\mathrm{sequence}\mathrm{wich}\mathrm{verify}{\mathrm{a}}_{\mathrm{n}+1}+{\mathrm{a}}_{\mathrm{n}}=\frac{1}{\mathrm{n}+1}\mathrm{\forall }\mathrm{n}$$$$\mathrm{calculate}\sum _{\mathrm{n}=0}^{\mathrm{\infty }}{\mathrm{a}}_{\mathrm{n}}{\mathrm{x}}^{\mathrm{n}}$$ Answered by Smail…

Question Number 96826 by bobhans last updated on 05/Jun/20 $$\mathrm{If}2\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}(\mathrm{x}-1)={\mathrm{x}}^2.\mathrm{determine}\mathrm{f}\left(\mathrm{x}\right)$$ Answered by john santu last updated on 05/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={px}^2+qx+r$$$$\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\:{px}^{\mathrm{2}}…

Question Number 96773 by abdomathmax last updated on 04/Jun/20 $$\mathrm{solve}{\mathrm{y}}^{{}^{″}}-\mathrm{y}=\frac{\mathrm{sinx}}{\mathrm{x}}$$ Answered by abdomathmax last updated on 05/Jun/20 $$\mathrm{let}\mathrm{solve}\mathrm{by}\mathrm{laplace}$$$$\left(\mathrm{e}\right)\Rightarrow\mathrm{L}\left(\mathrm{y}^{''} \right)−\mathrm{L}\left(\mathrm{y}\right)\:=\mathrm{L}\left(\frac{\mathrm{sinx}}{\mathrm{x}}\right)\:\Rightarrow \…