Question Number 30175 by abdo imad last updated on 17/Feb/18 $${prove}\:{that}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{n}+{k}}\:{is}\:{convergente}\:. \\ $$ Commented by abdo imad last updated on 21/Feb/18 $${we}\:{have}\:{u}_{{n}}…
Question Number 161202 by qaz last updated on 14/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left(\frac{\mathrm{k}}{\mathrm{n}}\right)^{\mathrm{n}} =? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161186 by mathlove last updated on 13/Dec/21 Answered by Rasheed.Sindhi last updated on 13/Dec/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{2}}\:{x}+\mathrm{10}}{\:\sqrt{\mathrm{2}}\:{x}−\mathrm{11}}\right)^{\frac{\mathrm{2}{x}−\mathrm{1}}{{x}+\mathrm{1}}} \\ $$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\cancel{{x}}\left(\sqrt{\mathrm{2}}\:+\frac{\mathrm{10}}{{x}}\right)}{\:\cancel{{x}}\left(\sqrt{\mathrm{2}}\:−\frac{\mathrm{11}}{{x}}\right)}\right)^{\frac{\cancel{{x}}\left(\mathrm{2}−\frac{\mathrm{1}}{{x}}\right)}{\cancel{{x}}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)}} \\ $$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{2}}\:+\frac{\mathrm{10}}{{x}}}{\:\sqrt{\mathrm{2}}\:−\frac{\mathrm{11}}{{x}}}\right)^{\frac{\mathrm{2}−\frac{\mathrm{1}}{{x}}}{\mathrm{1}+\frac{\mathrm{1}}{{x}}}} \\…
Question Number 30089 by tawa tawa last updated on 16/Feb/18 $$\mathrm{prove}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{or}\:\mathrm{divergence}\:\mathrm{of}\:\:\:\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}}\right)_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 95601 by mehran last updated on 26/May/20 $$\mathrm{1}{z} \\ $$$$ \\ $$$$\mathrm{1} \\ $$ Commented by john santu last updated on 26/May/20 $$\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{meant}?…
Question Number 161133 by qaz last updated on 12/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{n}}\right)}=? \\ $$ Answered by ArielVyny last updated on 12/Dec/21 $$\frac{\mathrm{1}}{{n}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{{x}\left({x}+\frac{\mathrm{1}}{{n}}\right)}=\int_{\mathrm{0}}…
Question Number 161111 by cortano last updated on 12/Dec/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} +\mathrm{2cos}\:{x}−\mathrm{2}}{{x}^{\mathrm{4}} }\:=\:\frac{\mathrm{1}}{{a}} \\ $$$$\:\:\:\:{a}=? \\ $$ Commented by blackmamba last updated on 12/Dec/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 29974 by hanieert last updated on 14/Feb/18 $$\sqrt{\mathrm{5}=?} \\ $$ Answered by MJS last updated on 14/Feb/18 $$ \\ $$$$\mathrm{2}.\mathrm{2360679774}… \\ $$ Terms…
Question Number 161014 by sdfg last updated on 10/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161002 by bobhans last updated on 10/Dec/21 $$\:\:\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ax}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{2x}}\:\sqrt{\mathrm{1}+\mathrm{bx}}\:−\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\mathrm{then}\:\mathrm{a}×\mathrm{b}\:=? \\ $$ Answered by blackmamba last updated on 11/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{ax}}{\left(\mathrm{1}+\frac{\mathrm{2}{x}}{\mathrm{3}}\right)\left(\mathrm{1}+\frac{{bx}}{\mathrm{2}}\right)−\mathrm{1}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\…