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Category: Arithmetic

n-0-2-1-2n-1-2n-1-2-

Question Number 90009 by M±th+et£s last updated on 20/Apr/20 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

1-2-1-3-2-2-3-5-3-2-5-7-n-2-2n-1-2n-1-

Question Number 155465 by cortano last updated on 01/Oct/21 $$\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{1}×\mathrm{3}}+\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}×\mathrm{5}}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{5}×\mathrm{7}}+…+\frac{\mathrm{n}^{\mathrm{2}} }{\left(\mathrm{2n}−\mathrm{1}\right)\left(\mathrm{2n}+\mathrm{1}\right)}= \\ $$ Answered by Ar Brandon last updated on 03/Oct/21 $${S}=\underset{{k}=\mathrm{1}}…

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Question Number 155428 by ajfour last updated on 30/Sep/21 $${simplify} \\ $$$${t}=\left(\frac{\mathrm{26}}{\mathrm{3}\sqrt{\mathrm{3}}}+\mathrm{5}\right)^{\mathrm{1}/\mathrm{3}} −\left(\frac{\mathrm{26}}{\mathrm{3}\sqrt{\mathrm{3}}}−\mathrm{5}\right)^{\mathrm{1}/\mathrm{3}} \\ $$ Answered by peter frank last updated on 30/Sep/21 $$\mathrm{t}=\left(\frac{\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}}}{\mathrm{3}\sqrt{\mathrm{3}}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} −\left(\frac{\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}}{\mathrm{3}\sqrt{\mathrm{3}}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question-89852

Question Number 89852 by M±th+et£s last updated on 19/Apr/20 Answered by mr W last updated on 19/Apr/20 $${F}_{{n}} =\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\varphi^{{n}} −\psi^{{n}} \right)\:{with} \\ $$$$\varphi=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}},\:\psi=\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}=\mathrm{1}−\varphi=−\frac{\mathrm{1}}{\varphi} \\ $$$${x}^{{n}}…