Question Number 3105 by prakash jain last updated on 04/Dec/15 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{next}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{below}\:\mathrm{sequence} \\ $$$$\mathrm{1},\mathrm{3},\mathrm{9},\mathrm{27},\mathrm{81},\mathrm{243},\mathrm{729},\:\mathrm{2123},\:\mathrm{5857},? \\ $$ Commented by Filup last updated on 04/Dec/15 $$\mathrm{3}^{\mathrm{10}} ? \\…
Question Number 3077 by Filup last updated on 04/Dec/15 $$\mathrm{Read}\:\mathrm{the}\:\mathrm{following}: \\ $$$$ \\ $$$${S}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{n}^{{i}!} \\ $$$${S}={n}^{\mathrm{1}} +{n}^{\mathrm{1}×\mathrm{2}} +{n}^{\mathrm{1}×\mathrm{2}×\mathrm{3}} +… \\ $$$${S}={n}^{\mathrm{1}} \left(\mathrm{1}+{n}^{\mathrm{2}} +{n}^{\mathrm{2}×\mathrm{3}}…
Question Number 68589 by peter frank last updated on 13/Sep/19 Answered by $@ty@m123 last updated on 14/Sep/19 $$\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)} \\ $$$$=\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\:\left(\:\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{1}}\right) \\…
Question Number 3052 by Filup last updated on 04/Dec/15 $$\mathrm{Ever}\:\mathrm{used}\:\mathrm{Arrow}\:\mathrm{Notation}? \\ $$$$ \\ $$$$\mathrm{if}\:\mathrm{my}\:\mathrm{memory}\:\mathrm{is}\:\mathrm{correct}: \\ $$$$\mathrm{3}\uparrow\mathrm{3}=\mathrm{3}×\mathrm{3}×\mathrm{3}=\mathrm{3}^{\mathrm{3}} \\ $$$$\mathrm{3}\uparrow\uparrow\mathrm{3}=\left(\mathrm{3}\uparrow\mathrm{3}\right)\uparrow\mathrm{3}=\mathrm{3}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{3}} \\ $$$$\mathrm{etc}. \\ $$ Commented…
Question Number 3001 by Filup last updated on 02/Dec/15 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{evaluate}: \\ $$$${S}=\underset{{i}={k}} {\overset{{n}} {\sum}}\:^{{n}} {C}_{{i}} \\ $$ Commented by Rasheed Soomro last updated on 02/Dec/15…
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Question Number 2930 by Filup last updated on 30/Nov/15 $$\mathrm{Prove}\:\mathrm{that}\:\Gamma\left({i}\right)=−{i}\left({i}\right)! \\ $$$$\mathrm{where}\:{i}=\sqrt{−\mathrm{1}} \\ $$ Commented by 123456 last updated on 02/Dec/15 $$\Gamma\left({z}\right)\Gamma\left(\mathrm{1}−{z}\right)=\frac{\pi}{\mathrm{sin}\:\pi{z}} \\ $$$$\Gamma\left({z}\right)\Gamma\left(−{z}\right)=−\frac{\pi}{{z}\:\mathrm{sin}\:\pi{z}} \\…
Question Number 133989 by Mamifere last updated on 26/Feb/21 $$\frac{{x}}{{x}\mathrm{2}+\mathrm{1}}<{arctan}\left({x}\right)<{x} \\ $$$$ \\ $$ Answered by Ñï= last updated on 26/Feb/21 $${Let}\:{f}\left({x}\right)={tan}^{−\mathrm{1}} {x} \\ $$$${we}\:{have}\:{f}\left({x}\right)−{f}\left(\mathrm{0}\right)={f}\left(\xi\right)'\left({x}−\mathrm{0}\right)…
Question Number 133916 by shaker last updated on 25/Feb/21 Answered by TheSupreme last updated on 25/Feb/21 $${S}_{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{e}^{{kx}} +{e}^{−{kx}} }{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}\left\{\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left({e}^{{x}} \right)^{{k}}…
Question Number 68349 by peter frank last updated on 09/Sep/19 Answered by mr W last updated on 09/Sep/19 $${w}_{{new}} =\mathrm{1}.\mathrm{03}{w}\:\:\:\left(\mathrm{3\%}\:{more}={factor}\:\mathrm{1}.\mathrm{03}\right) \\ $$$${d}_{{new}} =\mathrm{0}.\mathrm{975}{d}\:\:\:\left(\mathrm{2}.\mathrm{5\%}\:{less}={factor}\:\mathrm{0}.\mathrm{975}\right) \\ $$$${t}_{{new}}…