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 $${x}\:{and}\:{y}\:{are}\:{reals}\left({or}\:{complex}\right)\:{let}\:{put}\:{x}^{\left(\mathrm{0}\right)} =\mathrm{1}\:,{x}^{\left(\mathrm{1}\right)} ={x} \\ $$$${x}^{\left(\mathrm{2}\right)} ={x}\left({x}−\mathrm{1}\right)…..{x}^{\left({n}\right)} ={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…\left({x}−{n}+\mathrm{1}\right){prove}\:{that} \\ $$$$\left({x}+{y}\right)^{\left({n}\right)} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:\:{x}^{\left({n}−{k}\right)}…
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Question Number 138552 by mnjuly1970 last updated on 14/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{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
Question Number 7482 by kishanjith last updated on 31/Aug/16 $$\int\frac{\left(\mathrm{1}+{x}\right)^{−\mathrm{2}/\mathrm{3}} }{\left(\mathrm{1}+{x}\right)}{dx} \\ $$ Answered by sandy_suhendra last updated on 31/Aug/16 $$=\int\left(\mathrm{1}−{x}\right)^{\frac{−\mathrm{5}}{\mathrm{3}}} {dx} \\ $$$${let}\:\:\:{U}=\mathrm{1}−{x}\: \\…
Question Number 138554 by cherokeesay last updated on 14/Apr/21 Answered by mr W last updated on 14/Apr/21 Commented by mr W last updated on 14/Apr/21…
Question Number 73017 by Rio Michael last updated on 05/Nov/19 $${find}\: \\ $$$$\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\:{x}\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\: \\ $$ Commented by mathmax by abdo last updated on…
Question Number 138548 by I want to learn more last updated on 14/Apr/21 Answered by nimnim last updated on 14/Apr/21 $${Let}\:{the}\:{centre}\:{of}\:{the}\:{circle}\:{be}\:{C}\left({h},{k}\right) \\ $$$${Since},\:{it}\:{touches}\:{the}\:{x}−{axis}\:{at}\:{P}\left(−\mathrm{3},\mathrm{0}\right), \\ $$$$\:{CP}\bot\:{x}−{axis}\:{and}\:{h}=−\mathrm{3}…
Question Number 7478 by Yozzia last updated on 31/Aug/16 $${Find}\:{the}\:{value}\:{of}\:\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)\:\:{if}\:\:{x}\left({x}−\mathrm{3}\right)=−\mathrm{1}. \\ $$ Answered by Rasheed Soomro last updated on 31/Aug/16 $$\:\:\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)\:\:{if}\:\:{x}\left({x}−\mathrm{3}\right)=−\mathrm{1}…