Question Number 73033 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{N}^{\mathrm{2}} \:\:\:\:{x}\left({x}+\mathrm{1}\right)=\mathrm{4}{y}\left({y}+\mathrm{1}\right) \\ $$ Answered by mind is power last updated on 05/Nov/19 $$\Leftrightarrow\mathrm{4x}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{16y}\left(\mathrm{y}+\mathrm{1}\right)…
Question Number 73030 by Tanmay chaudhury last updated on 05/Nov/19 Answered by Tanmay chaudhury last updated on 05/Nov/19 $$\int_{\mathrm{0}} ^{\mathrm{4}} \frac{{ln}\mathrm{2}}{{lnx}}−\frac{{ln}\mathrm{2}×{ln}\mathrm{2}}{{lnx}×{lnx}×{ln}\mathrm{2}}{dx} \\ $$$${ln}\mathrm{2}\int_{\mathrm{2}} ^{\mathrm{4}} \frac{\mathrm{1}}{{lnx}}−\frac{\mathrm{1}}{\left({lnx}\right)^{\mathrm{2}}…
Question Number 138564 by DomaPeti last updated on 14/Apr/21 $${y}\centerdot{y}'=\mathrm{0}.\mathrm{5}\centerdot\left(\mathrm{1}+{y}\centerdot{c}_{\mathrm{1}} \right)^{\mathrm{2}} \centerdot{c}_{\mathrm{2}} +\mathrm{0}.\mathrm{5} \\ $$$$ \\ $$$${y}=? \\ $$ Answered by mr W last updated…
Question Number 73031 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{N}^{\mathrm{2}} \:\:\:\mathrm{3}{x}^{\mathrm{3}} \:+{xy}\:+\mathrm{4}{y}^{\mathrm{3}} \:=\mathrm{349} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73028 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:\sum_{\mathrm{1}\leqslant{i}\leqslant{n}\:{and}\:\mathrm{1}\leqslant{j}\leqslant{n}} \:\:{min}\left({i},{j}\right) \\ $$ Answered by mind is power last updated on 05/Nov/19 $$=\underset{\mathrm{i}=\mathrm{1}}…
Question Number 73029 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\forall\left({n},{p},{q}\right)\in{N}^{\mathrm{3}} \:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{p}} ^{{k}} \:{C}_{{q}} ^{{n}−{k}} \:\:\:={C}_{{p}+{q}} ^{{n}} \\ $$$${conclude}\:{that}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\left({C}_{{n}} ^{{k}}…
Question Number 138560 by Raxreedoroid last updated on 14/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left(\mathrm{ln}\:\left({n}+\mathrm{1}\right)−\mathrm{ln}\:\left({n}\right)\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 14/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 73027 by mathmax by abdo last updated on 05/Nov/19 $${x}\:{and}\:{y}\:{are}\:{reals}\left({or}\:{complex}\right)\:{let}\:{put}\:{x}^{\left(\mathrm{0}\right)} =\mathrm{1}\:,{x}^{\left(\mathrm{1}\right)} ={x} \\ $$$${x}^{\left(\mathrm{2}\right)} ={x}\left({x}−\mathrm{1}\right)…..{x}^{\left({n}\right)} ={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…\left({x}−{n}+\mathrm{1}\right){prove}\:{that} \\ $$$$\left({x}+{y}\right)^{\left({n}\right)} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:\:{x}^{\left({n}−{k}\right)}…
Question Number 73021 by TawaTawa last updated on 05/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138552 by mnjuly1970 last updated on 14/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:\:\:\:\:{mathemayics}\:… \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({tan}\left({x}\right)\right)}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\frac{\mathrm{1}}{{e}}\right) \\ $$$$\:\:……. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com