Question Number 9237 by geovane10math last updated on 25/Nov/16 $${About}\:{the}\:{Euler}-{Mascheroni}\:{constant} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\gamma\:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:−\:\mathrm{ln}\:{n}\right) \\ $$$${Why}\:{the}\:{limit}\:{converges}\:{if} \\ $$$$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:−\:\mathrm{ln}\:{n}\right)\:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:−\:\underset{{n}\rightarrow\infty}…
Question Number 9232 by geovane10math last updated on 24/Nov/16 $$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+…+\:{n}\:=\:\frac{{n}\left({n}\:+\:\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} \:+\mathrm{3}^{\mathrm{2}} \:+…+\:{n}^{\mathrm{2}} \:=\:\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$$$\mathrm{1}^{{x}} \:+\:\mathrm{2}^{{x}} \:+\:\mathrm{3}^{{x}} \:+…+\:=\:{n}^{{x}} \:=\:\mathrm{Formula}? \\ $$$${x}\:\in\:\mathbb{R} \\…
Question Number 140285 by mohammad17 last updated on 06/May/21 $$\int\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }} \\ $$ Commented by mohammad17 last updated on 06/May/21 $$?????? \\ $$ Commented by…
Question Number 9215 by arinto27 last updated on 23/Nov/16 Answered by ridwan balatif last updated on 23/Nov/16 $$\mathrm{benda}\:\mathrm{dititik}\:\mathrm{tertinggi}\:\mathrm{memiliki}\:\mathrm{energi}\:\mathrm{potensial}\:\mathrm{sebesar}\:\mathrm{E}_{\mathrm{o}} \\ $$$$\mathrm{dimana}\:\mathrm{E}_{\mathrm{o}} =\mathrm{mgh}\:\left(\mathrm{misalkan}\:\mathrm{dititik}\:\mathrm{tertinggi},\:\mathrm{kita}\:\mathrm{beri}\:\mathrm{nama}\:\mathrm{titik}\:\mathrm{A}\right) \\ $$$$\mathrm{EM}_{\mathrm{A}} =\mathrm{EM}_{\mathrm{p}} \\…
Question Number 140281 by mohammad17 last updated on 06/May/21 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{tan}^{−\mathrm{1}} \left(\sqrt{{tanx}}\right)}{{tanx}}{dx} \\ $$ Commented by mohammad17 last updated on 06/May/21 $$?????? \\ $$…
Question Number 9201 by geovane10math last updated on 22/Nov/16 $$\int{x}!\:{dx}\:=\:? \\ $$$$ \\ $$ Commented by FilupSmith last updated on 23/Nov/16 $$\Gamma\left({x}\right)=\left({x}−\mathrm{1}\right)! \\ $$$$\psi\left({x}\right)=\frac{\Gamma'\left({x}\right)}{\Gamma\left({x}\right)} \\…
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Question Number 74703 by Mr. K last updated on 29/Nov/19 $${let}\:\boldsymbol{{b}}\:{and}\:\boldsymbol{{r}}\:{be}\:{two}\:{positive}\:{prime}\: \\ $$$${numbers}\:{such}\:{that}\:{b}\neq{r}\:{and}\:{b}×{r}\:{is} \\ $$$${a}\:{divisor}\:{of}\:\mathrm{138}.\:{Consider}\:{an}\: \\ $$$${arithmetic}\:{progression}\:{in}\:{which} \\ $$$${the}\:{first}\:{term}\:{is}\:\boldsymbol{{b}},\:{the}\:{ratio}\:{is}\:\boldsymbol{{r}} \\ $$$${and}\:{the}\:{fourth}\:{term}\:{is}\:\mathrm{71}.\:{What}\:{is}\:{the} \\ $$$${value}\:{of}\:\boldsymbol{{b}}+\boldsymbol{{r}}? \\ $$…