Question Number 157942 by mathlove last updated on 30/Oct/21 Commented by cortano last updated on 30/Oct/21 $$\left(\mathrm{1}\right){x}+\mathrm{2}{x}+\mathrm{3}{x}+…+{nx}=\frac{{n}}{\mathrm{2}}\left({nx}+{x}\right) \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\frac{{x}}{\mathrm{2}}\right)\left(\mathrm{1}+\frac{\mathrm{2}{x}}{\mathrm{2}}\right)\left(\mathrm{1}+\frac{\mathrm{3}{x}}{\mathrm{2}}\right)…\left(\mathrm{1}+\frac{{nx}}{\mathrm{2}}\right)−\mathrm{1}}{\frac{{n}}{\mathrm{2}}\left({nx}+{x}\right)} \\ $$$${L}=\frac{\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}.\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{2}}+…+\frac{{n}}{\mathrm{2}}\right){x}}{{x}} \\ $$$${L}=\frac{\mathrm{2}}{{n}\left({n}+\mathrm{1}\right)}.\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}\right)…
Question Number 92340 by jagoll last updated on 06/May/20 $$\underset{\mathrm{i}\:=\:\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\mathrm{5}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{i}} } +\mathrm{3}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{i}} } }{\mathrm{2}}\:=\: \\ $$ Commented by john santu last updated on…
Question Number 26768 by abdo imad last updated on 29/Dec/17 $${find}\:{the}\:{nature}\:{of}\:{U}_{{n}} \:\:=\sum_{{p}=\mathrm{0}} ^{{p}={n}} \:\:\frac{\mathrm{1}}{{C}_{{n}} ^{{p}} }\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 26764 by abdo imad last updated on 29/Dec/17 $${find}\:\:{lim}_{{n}−>\propto} \:\frac{\mathrm{1}}{{n}}\:{ln}\left(\:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:\left(\mathrm{1}−\:\frac{{k}}{{n}}\right)\right). \\ $$ Commented by prakash jain last updated on 29/Dec/17 $$\underset{{k}=\mathrm{1}}…
Question Number 26761 by abdo imad last updated on 29/Dec/17 $${let}\:{put}\:\:{s}_{{n}} =\:\frac{\sum_{{k}=\mathrm{0}} ^{{k}={n}} \left(\mathrm{2}{k}+\mathrm{1}\right)}{\sum_{{k}=\mathrm{1}} ^{{k}={n}} \:{k}} \\ $$$${find}\:{lim}_{{n}−>\propto} {s}_{{n}} \\ $$ Answered by prakash jain…
Question Number 92291 by jagoll last updated on 06/May/20 $$ \\ $$$$\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{ln}\:\mathrm{x}} \:=?\: \\ $$ Commented by abdomathmax last updated on 06/May/20 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}−{x}\right)^{{lnx}}…
Question Number 92289 by jagoll last updated on 06/May/20 $$ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{ln}\left(\frac{\left(\mathrm{3}+\mathrm{e}\right)^{\mathrm{x}} }{\mathrm{2x}}\right)\:? \\ $$ Commented by mathmax by abdo last updated on 06/May/20…
Question Number 26751 by abdo imad last updated on 28/Dec/17 $${by}\:{using}\:{fourier}\:{serie}\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\propto} \:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by abdo imad last updated on 30/Dec/17 $${we}\:{know}\:{that}\:/{x}/=\:\frac{\pi}{\mathrm{2}}\:−\frac{\mathrm{4}}{\pi}\:\sum_{{p}=\mathrm{0}}…
Question Number 26749 by abdo imad last updated on 28/Dec/17 $${let}\:{give}\:\:{S}_{{n}} \:=\:\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\:\frac{\mathrm{1}}{{i}^{\mathrm{2}} {j}^{\mathrm{2}} }\:\:\:{find}\:{lim}_{{n}−>\propto} \:\:{S}_{{n}} \:\:. \\ $$ Commented by abdo imad last updated…
Question Number 157803 by cortano last updated on 28/Oct/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{tan}\:\left(\mathrm{tan}\:{x}\right)−\left(\mathrm{tan}\:{x}\right)^{\mathrm{2}} }{{x}^{\mathrm{6}} }\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com