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Question Number 8175 by prakash jain last updated on 02/Oct/16 $$\mathrm{Prove} \\ $$$$\frac{\mathrm{4}^{{n}} }{{n}}<\:^{\mathrm{2}{n}} {C}_{{n}} \:\mathrm{for}\:\mathrm{all}\:{n}\geqslant\mathrm{4}\:\mathrm{and}\:{n}\in\mathbb{Z}^{+} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8174 by prakash jain last updated on 02/Oct/16 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{infinite}\:\mathrm{prime} \\ $$$$\mathrm{numbers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\mathrm{10}^{{n}} +\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73708 by Faradtimmy last updated on 15/Nov/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 73707 by Faradtimmy last updated on 15/Nov/19 Commented by Faradtimmy last updated on 16/Nov/19 $${pls}\:{help}\:{me}\:{to}\:{solve}\:{it} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 8168 by aungnaingsoe last updated on 02/Oct/16 $${Find}\:{the}\:{coefficient}\:{of}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)…\left(\mathrm{1}+{x}^{{n}} \right). \\ $$ Commented by Rasheed Soomro last updated on 02/Oct/16…
Question Number 8164 by 666225 last updated on 02/Oct/16 $${if}\:\boldsymbol{{p}}\:{is}\:{prima}\:{show}\:{that}\:\sqrt{\boldsymbol{{p}}}\:{irasional} \\ $$ Commented by 123456 last updated on 02/Oct/16 $$\mathrm{1}\mid{p},{p}\mid{p},{p}>\mathrm{1} \\ $$$${p}\mid{a}^{\mathrm{2}} \Leftrightarrow{p}\mid{a} \\ $$…
Question Number 139232 by Dwaipayan Shikari last updated on 24/Apr/21 $${A}\:{man}\:{has}\:'{n}'\:{pair}\:{of}\:{black}\:{shoes}\:{and}\:'{m}' \\ $$$${pairs}\:{of}\:{brown}\:{shoes}.\:{Man}\:{hurriedly}\:{wear} \\ $$$${two}\:{shoes}.\:{What}\:{is}\:{probability}\:{that}\:{both}\:{of} \\ $$$${them}\:{are}\:{black}? \\ $$ Commented by mr W last updated…
Question Number 73697 by mathmax by abdo last updated on 14/Nov/19 $${find}\:{a}\:{formulae}\:{for}\:{calculus}\:{of}\:{arctan}\left({x}+{iy}\right) \\ $$ Commented by mathmax by abdo last updated on 15/Nov/19 $${we}\:{have}\:{proved}\:{that}\:{arctanz}\:=\frac{\mathrm{1}}{\mathrm{2}{i}}{ln}\left(\frac{\mathrm{1}+{iz}}{\mathrm{1}−{iz}}\right)\:\Rightarrow \\…