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Category: Algebra

Solve-the-system-of-equation-2x-y-z-8-equation-i-x-2-y-2-2z-2-14-equation-ii-3x-3-4y-3-z-3-195-equation-iii-

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-71926

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) \\…

i-n-1-3i-1-2-3-n-1-i-0-

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}:…

1-4-9-n-2-n-n-1-2n-1-6-

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}} \\…

1-2-3-2-5-2-2n-1-2-n-3-4n-2-1-

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…

Find-the-sum-of-n-terms-of-the-following-series-1-1-x-1-1-x-1-1-x-

Question Number 6329 by Rasheed Soomro last updated on 24/Jun/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{x}}}+\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{1}−\sqrt{\mathrm{x}}}+…. \\ $$ Commented by FilupSmith last updated on 24/Jun/16 $${s}\mathrm{equence}\:{x},\:\sqrt{{x}},\:{x}…\:\mathrm{can}\:\mathrm{be}\:\mathrm{given}\:\mathrm{by}: \\ $$$$\frac{{x}}{\mathrm{2}}\left(\mathrm{1}−\left(−\mathrm{1}\right)^{{n}+\mathrm{1}}…