Question Number 137473 by mr W last updated on 03/Apr/21 $${what}\:{is}\:{larger}?\:\mathrm{99}^{\mathrm{100}} \:{or}\:\mathrm{100}^{\mathrm{99}} ? \\ $$ Answered by MJS_new last updated on 03/Apr/21 $${n}^{{n}+\mathrm{1}} >\left({n}+\mathrm{1}\right)^{{n}} \:\forall\:{n}\geqslant\mathrm{3}…
Question Number 137476 by peter frank last updated on 03/Apr/21 Commented by MJS_new last updated on 03/Apr/21 $$\mathrm{but}\:\mathrm{this}\:\mathrm{is}\:\mathrm{not}\:\mathrm{mathematics}.\:\mathrm{I}\:\mathrm{can}\:\mathrm{easily}\:\mathrm{get} \\ $$$$\mathrm{the}\:\mathrm{answer}\:\frac{\mathrm{1804192}}{\mathrm{42413}}\:\mathrm{or}\:\mathrm{any}\:\mathrm{other}\:\mathrm{number}\:\mathrm{you} \\ $$$$\mathrm{prefer} \\ $$ Commented…
Question Number 137472 by mr W last updated on 03/Apr/21 $${solve} \\ $$$${x}^{\mathrm{3}} −\mathrm{2}\left[{x}\right]=\mathrm{5} \\ $$ Answered by MJS_new last updated on 03/Apr/21 $$\left(\mathrm{1}\right)\:\:\mathrm{1}<{x}<\mathrm{2} \\…
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Question Number 6393 by sanusihammed last updated on 25/Jun/16 $${Solve}\:{the}\:{system}\:{of}\:{equation}\: \\ $$$$\mathrm{2}{x}\:+\:{y}\:−\:{z}\:=\:\mathrm{8}\:\:\:\:\:\:…………\:{equation}\:\left({i}\right) \\ $$$${x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:……….\:\:{equation}\:\left({ii}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{3}\:} +\:\mathrm{4}{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:\:\:……..\:{equation}\:\left({iii}\right) \\ $$ Commented…
Question Number 71926 by TawaTawa last updated on 22/Oct/19 Commented by Prithwish sen last updated on 22/Oct/19 $$\boldsymbol{\mathrm{If}}\:\:!!\:\:\boldsymbol{\mathrm{means}}\:\boldsymbol{\mathrm{mere}}\:\boldsymbol{\mathrm{factorial}}\:\boldsymbol{\mathrm{than}}\:\mathrm{3002}!!\:\boldsymbol{\mathrm{must}} \\ $$$$\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{divisible}}\:\boldsymbol{\mathrm{by}}\:\mathrm{2003} \\ $$$$\boldsymbol{\mathrm{i}}.\boldsymbol{\mathrm{e}} \\ $$$$\:\:\:\:\:\mathrm{3092}!!\:\equiv\:\mathrm{0}\:\left(\boldsymbol{\mathrm{mod}}\:\mathrm{2003}\right) \\…
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Question Number 6354 by sanusihammed last updated on 24/Jun/16 $${i}\:=\:{n}−\mathrm{1} \\ $$$$\Sigma\:\:\mathrm{3}{i}\:\:\:\:\:=\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}^{{n}} \:−\:\mathrm{1}\right) \\ $$$${i}\:=\:\mathrm{0} \\ $$ Commented by nburiburu last updated on 24/Jun/16 $${doesn}'{t}\:{seem}\:{well}\:{writen}:…
Question Number 6351 by sanusihammed last updated on 24/Jun/16 $$\mathrm{1}\:+\:\mathrm{4}\:+\:\mathrm{9}\:+\:…….\:{n}^{\mathrm{2}} \:=\:\frac{{n}\left({n}\:+\:\mathrm{1}\right)\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)}{\mathrm{6}} \\ $$ Commented by prakash jain last updated on 24/Jun/16 $${proving}\:{for}\:{k}+\mathrm{1}\:{assuming}\:{result}\:{for}\:{k} \\ $$$$\frac{{k}\left({k}+\mathrm{1}\right)\left(\mathrm{2}{k}+\mathrm{1}\right)}{{k}}+\left({k}+\mathrm{1}\right)^{\mathrm{2}} \\…
Question Number 6353 by sanusihammed last updated on 24/Jun/16 $$\mathrm{1}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2}} \:+\:………\:+\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:=\:\frac{{n}}{\mathrm{3}}\left(\mathrm{4}{n}^{\mathrm{2}\:} −\:\mathrm{1}\right) \\ $$ Commented by prakash jain last updated on 24/Jun/16…