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Question Number 147334 by Tawa11 last updated on 19/Jul/21 $$\mathrm{If}\:\:\:\:\mathrm{log}_{\mathrm{6}} \mathrm{30}\:\:\:=\:\:\:\mathrm{a},\:\:\:\:\:\:\:\:\:\mathrm{log}_{\mathrm{15}} \mathrm{24}\:\:\:=\:\:\:\mathrm{b},\:\:\:\:\:\:\:\:\:\:\:\mathrm{evaluate}:\:\:\:\mathrm{log}_{\mathrm{12}} \mathrm{60} \\ $$ Commented by otchereabdullai@gmail.com last updated on 20/Jul/21 $$\mathrm{nice}! \\ $$…
Question Number 147294 by ArielVyny last updated on 19/Jul/21 $$\Sigma\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{4}} }=? \\ $$ Answered by mathmax by abdo last updated on 19/Jul/21 $$\sum_{\mathrm{n}=\mathrm{1}} ^{\infty}…
Question Number 147252 by mathlove last updated on 19/Jul/21 Answered by Olaf_Thorendsen last updated on 19/Jul/21 $${l}\:=\:\left(\frac{\mathrm{1}}{\mathrm{5}}+\left(\frac{\mathrm{1}}{\mathrm{5}}+\left(\frac{\mathrm{1}}{\mathrm{5}}+…\right)^{\mathrm{2}} \right)^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$$${l}\:=\:\left(\frac{\mathrm{1}}{\mathrm{5}}+{l}\right)^{\mathrm{2}} \\ $$$${l}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{5}}{l}+\frac{\mathrm{1}}{\mathrm{25}}\:=\:\mathrm{0} \\…
Question Number 81446 by john santu last updated on 13/Feb/20 $$\mathrm{given}\:\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{2}\:,\:\mathrm{a}_{\mathrm{2}} \:=\:\mathrm{3}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:+\:\frac{\mathrm{a}_{\mathrm{n}} }{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \:=? \\ $$ Commented by…
Question Number 146979 by ajfour last updated on 16/Jul/21 $${If}\:{there}\:{just}\:{were} \\ $$$$\:\:\mathrm{0},\pm\mathrm{1},\pm\mathrm{2},\pm\mathrm{3},\pm\mathrm{4},\pm{i} \\ $$$${in}\:{place}\:{of}\:{the}\:{decimal}\:{or} \\ $$$${binary}\:{equivalets}.. \\ $$ Commented by Rasheed.Sindhi last updated on 17/Jul/21…
Question Number 81311 by M±th+et£s last updated on 11/Feb/20 Commented by mind is power last updated on 11/Feb/20 $$\Gamma\left({n}+{x}\right)=\left({n}−\mathrm{1}+{x}\right)\left({n}−\mathrm{2}+{x}\right)…{x}\Gamma\left({x}\right)\:\: \\ $$$$\Gamma\left({n}+{x}\right)=\Gamma\left({x}\right)\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left({n}−{k}+{x}\right) \\ $$$$\Rightarrow\Gamma\left({n}+\mathrm{1}−\frac{{k}}{{n}}\right)=\Gamma\left(\mathrm{1}−\frac{{k}}{{n}}\right)\underset{{j}=\mathrm{1}}…
Question Number 15770 by arnabpapu550@gmail.com last updated on 13/Jun/17 $$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{last}\:\mathrm{two}\:\mathrm{digits}\:\mathrm{of}\:\:\mathrm{2}^{\mathrm{576}} \\ $$ Answered by Tinkutara last updated on 14/Jun/17 $$\mathrm{2}^{\mathrm{576}} \:=\:\mathrm{2}^{\mathrm{4}×\mathrm{144}} \:\equiv\:\mathrm{6} \\ $$$$\mathrm{Last}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{6}. \\…
Question Number 81222 by M±th+et£s last updated on 10/Feb/20 Answered by mind is power last updated on 10/Feb/20 $$\:\:_{\mathrm{1}} {F}_{{a}} \left(\mathrm{1};\frac{{a}+{b}}{{a}},\frac{{a}+{b}−\mathrm{1}}{{a}},…….,\frac{{b}+\mathrm{1}}{{a}};\frac{{x}}{{a}^{{a}} }\right) \\ $$$$=\underset{{k}\geqslant\mathrm{0}} {\sum}\frac{{k}!}{\underset{{j}=\mathrm{0}}…
Question Number 15671 by tawa tawa last updated on 12/Jun/17 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematcal}\:\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:\mathrm{n}}\:=\:\frac{\mathrm{2n}}{\mathrm{n}\:+\:\mathrm{1}} \\ $$ Answered by icyfalcon999 last updated on 12/Jun/17 $$\left.\mathrm{1}\right)\mathrm{proving}\:\mathrm{that}\:\mathrm{the}\:\mathrm{statement}\:\mathrm{true}\:\mathrm{when}\:\mathrm{n}=\mathrm{1} \\ $$$$\mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{\mathrm{2}\left(\mathrm{1}\right)}{\mathrm{1}+\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{2}}=\mathrm{1}=\mathrm{L}.\mathrm{H}.\mathrm{S}.…