Question Number 22768 by math solver last updated on 22/Oct/17 Commented by math solver last updated on 22/Oct/17 $${find}\:{the}\:{sum}\:{of}\:{infinite}\:{terms}\:{of}\: \\ $$$${the}\:{series}\:.. \\ $$ Commented by…
Question Number 153839 by liberty last updated on 11/Sep/21 Commented by mathdanisur last updated on 11/Sep/21 $$\mathrm{x}\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+…+\mathrm{4041}}\right)\:=\:\mathrm{4041} \\ $$$$\blacktriangle\:\boldsymbol{\mathrm{A}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+…+\boldsymbol{\mathrm{n}}}\:=\:\frac{\mathrm{2}\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{n}}\:+\:\mathrm{1}} \\ $$$$\boldsymbol{\mathrm{n}}\:=\:\mathrm{4041}\:\Rightarrow\:\boldsymbol{\mathrm{A}}\:=\:\frac{\mathrm{2}\:\centerdot\:\mathrm{4041}}{\mathrm{4041}\:+\:\mathrm{1}}\:=\:\frac{\mathrm{2}\:\centerdot\:\mathrm{4041}}{\mathrm{2}\:\centerdot\:\mathrm{2021}}\:=\:\frac{\mathrm{4041}}{\mathrm{2021}} \\ $$$$\Rightarrow\:\boldsymbol{\mathrm{x}}\:\centerdot\:\frac{\mathrm{4041}}{\mathrm{2021}}\:=\:\mathrm{4041}\:\Rightarrow\:\boldsymbol{\mathrm{x}}\:=\:\mathrm{2021}\:\blacktriangle \\ $$…
Question Number 153829 by mathdanisur last updated on 10/Sep/21 $$\mathrm{L}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{6}}{\pi^{\mathrm{2}} }\left(\mathrm{Li}_{\mathrm{2}} \left(\mathrm{x}\right)\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{log}\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{1}-\mathrm{x}\right)\right. \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{L}\left(\mathrm{x}\right)\centerdot\mathrm{Li}_{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 153817 by eman_64 last updated on 10/Sep/21 Commented by puissant last updated on 10/Sep/21 $${Correct}..! \\ $$ Commented by alisiao last updated on…
Question Number 153808 by mathdanisur last updated on 10/Sep/21 $$\mathrm{If}\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}<\mathrm{1}\:\:\mathrm{then}: \\ $$$$\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\left(\frac{\mathrm{1}\:-\:\mathrm{xyz}}{\mathrm{1}\:+\:\mathrm{xyz}}\right)^{\mathrm{3}} \mathrm{dxdydz}\:\geqslant\:\left(\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\frac{\mathrm{1}\:-\:\mathrm{x}^{\mathrm{3}} }{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{3}} }\:\mathrm{dx}\right)^{\mathrm{3}} \\ $$…
Question Number 22739 by Tinkutara last updated on 22/Oct/17 $${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:…\:+\:{C}_{{n}} {x}^{{n}} , \\ $$$${Prove}\:{that}\:\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left({i}\:+\:{j}\right){C}_{{i}} {C}_{{j}} \:=…
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Question Number 22726 by math solver last updated on 22/Oct/17 Commented by math solver last updated on 24/Oct/17 $$\:{solve}\:{q}.\mathrm{8}? \\ $$ Commented by math solver…
Question Number 88252 by A8;15: last updated on 09/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 88251 by A8;15: last updated on 09/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com