Question Number 144929 by gsk2684 last updated on 30/Jun/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\: \\ $$$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{\mathrm{n}}}{\mathrm{n}^{\mathrm{2}} }\right)^{\mathrm{n}} \:\: \\ $$ Answered by mathmax by abdo last updated on…
Question Number 79374 by TawaTawa last updated on 24/Jan/20 Answered by mind is power last updated on 24/Jan/20 $${cv}\:\sim\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:{Riemann} \\ $$$$\frac{{n}−\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}=\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{−\mathrm{3}}{−\mathrm{1}.\mathrm{1}.\left({n}+\mathrm{2}\right)}−\frac{\mathrm{4}}{\left(−\mathrm{2}\right)\left(−\mathrm{1}\right)\left({n}+\mathrm{3}\right)} \\ $$$$=\underset{{n}\geqslant\mathrm{1}} {\sum}\left\{−\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{\mathrm{3}}{\left({n}+\mathrm{2}\right)}−\frac{\mathrm{2}}{\left({n}+\mathrm{3}\right)}\right\}…
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Question Number 79359 by ahmadshahhimat775@gmail.com last updated on 24/Jan/20 Commented by mathmax by abdo last updated on 24/Jan/20 $${let}\:{A}_{{n}} =\frac{\left({n}!\right)^{\frac{\mathrm{1}}{{n}}} }{{n}}\:\:{we}\:{have}\:{n}!\:\sim{n}^{{n}} {e}^{−{n}} \sqrt{\mathrm{2}\pi{n}}\left(\:{stirling}\:{formulae}\right)\:\Rightarrow \\ $$$$\left({n}!\right)^{\frac{\mathrm{1}}{{n}}}…
Question Number 144816 by liberty last updated on 29/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{6x}^{\mathrm{2}} }−\left(\mathrm{1}+\mathrm{7x}\right)}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}−\mathrm{3}\right)}\:=? \\ $$ Answered by imjagoll last updated on 29/Jun/21 $$\:=−\frac{\mathrm{1}}{\mathrm{3}}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{6x}^{\mathrm{2}} \right)−\left(\mathrm{1}+\mathrm{14x}+\mathrm{49x}^{\mathrm{2}}…
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Question Number 79236 by jagoll last updated on 23/Jan/20 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\mathrm{x}\left\{\mathrm{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}} \right\}=? \\ $$ Commented by mathmax by abdo last updated on 23/Jan/20 $${let}\:{A}\left({x}\right)={x}\left\{{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \right\}\:\:{we}\:{have}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}}…
Question Number 144744 by mondlihk last updated on 28/Jun/21 Answered by Olaf_Thorendsen last updated on 28/Jun/21 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\frac{{x}−\mathrm{1}}{{y}−\mathrm{1}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{1}}{\mathrm{2}{x}−\mathrm{1}}\:=\:\mathrm{1} \\ $$ Terms of Service Privacy…
Question Number 144622 by phally last updated on 27/Jun/21 Answered by alcohol last updated on 27/Jun/21 $${e}^{\frac{\mathrm{1}}{\mathrm{2}{a}}} \\ $$ Answered by mathmax by abdo last…