Question Number 3193 by Filup last updated on 07/Dec/15 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}: \\ $$$$\underset{{i}={a}} {\overset{{n}} {\sum}}{i}=\underset{{i}={a}} {\overset{{n}} {\prod}}{i}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({n},\:{a}\right)\in\mathbb{Z} \\ $$ Commented by Filup last updated on 07/Dec/15…
Question Number 68710 by peter frank last updated on 15/Sep/19 Commented by Prithwish sen last updated on 15/Sep/19 $$\mathrm{x}+\mathrm{y}=\mathrm{0}…….\left(\mathrm{i}\right) \\ $$$$\mathrm{x}−\mathrm{y}=−\mathrm{4}……\left(\mathrm{ii}\right) \\ $$$$\mathrm{solving}\:\mathrm{x}=−\mathrm{2},\mathrm{y}=\mathrm{2} \\ $$$$\therefore\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{center}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{is}}\:\left(−\mathrm{2},\mathrm{2}\right)…
Question Number 3148 by Filup last updated on 06/Dec/15 $${Solve}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{t}^{{k}} }{{k}^{{t}} }\:{for}\:{n}=\mathrm{10},\:{t}=\mathrm{2} \\ $$ Commented by prakash jain last updated on 06/Dec/15 $$\frac{\mathrm{2}^{\mathrm{1}}…
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}} \\…