Question Number 68783 by peter frank last updated on 15/Sep/19 Commented by peter frank last updated on 22/Sep/19 $${thank}\:{you}\: \\ $$ Commented by ajfour last…
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Question Number 68773 by rajesh4661kumar@gmail.com last updated on 15/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 68775 by rajesh4661kumar@gmail.com last updated on 15/Sep/19 Answered by $@ty@m123 last updated on 15/Sep/19 $${Let}\:{a}\:{be}\:\:{the}\:{first}\:{term}\:{and}\:{d}\:{be}\:{the} \\ $$$${common}\:{difference}\:{of}\:{AP}. \\ $$$${a}+\left({p}−\mathrm{1}\right){d}={A}\:…\left(\mathrm{1}\right) \\ $$$${a}+\left({q}−\mathrm{1}\right){d}={AR}\:\:….\left(\mathrm{2}\right) \\ $$$${a}+\left({r}−\mathrm{1}\right){d}={AR}^{\mathrm{2}}…
Question Number 3204 by Filup last updated on 07/Dec/15 $$\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{i}!=\mathrm{1}×\left(\mathrm{1}×\mathrm{2}\right)×…×\left(\mathrm{1}×\mathrm{2}×…×{n}\right) \\ $$$$=\mathrm{1}^{{n}} \mathrm{2}^{{n}−\mathrm{1}} \mathrm{3}^{{n}−\mathrm{2}} …\left({n}−\mathrm{1}\right)^{\mathrm{2}} {n} \\ $$$$\therefore\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{i}!=\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\left({n}−{i}+\mathrm{1}\right)^{{i}} \\…
Question Number 68732 by ravi Raj last updated on 15/Sep/19 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 3198 by Filup last updated on 07/Dec/15 $$\underset{{i}={a}} {\overset{{n}} {\prod}}{i}=?\:\:\:\:\:\mathrm{for}\:\mid{i}\mid<\mathrm{1},\:\:{a}\in\mathbb{R} \\ $$ Commented by Filup last updated on 07/Dec/15 $$=\frac{\mathrm{1}}{{a}}×\frac{\mathrm{1}}{{a}+\mathrm{1}}×…×\frac{\mathrm{1}}{{n}} \\ $$$$=\frac{\mathrm{1}}{\left(\frac{{n}!}{\left({a}−\mathrm{1}\right)!}\right)} \\…
Question Number 3193 by Filup last updated on 07/Dec/15 $$\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}}…