Question Number 61425 by naka3546 last updated on 02/Jun/19 Commented by alphaprime last updated on 02/Jun/19 9 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61424 by Tawa1 last updated on 02/Jun/19 Answered by mr W last updated on 02/Jun/19 Commented by mr W last updated on 02/Jun/19…
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Question Number 126954 by bramlexs22 last updated on 25/Dec/20 $$\:\:\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{18}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{7}\pi}{\mathrm{18}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{17}\pi}{\mathrm{18}}\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 25/Dec/20 $$\mathrm{2}{cos}\left(\frac{\mathrm{12}\pi}{\mathrm{36}}\right){cos}\left(\frac{\pi}{\mathrm{18}}\right)+{cos}\left(\frac{\mathrm{17}\pi}{\mathrm{18}}\right) \\ $$$$={cos}\left(\frac{\pi}{\mathrm{18}}\right)+{cos}\left(\frac{\mathrm{17}\pi}{\mathrm{18}}\right)=\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{2}}\right){cos}\left(\frac{\mathrm{8}\pi}{\mathrm{18}}\right)=\mathrm{0} \\ $$…
Question Number 126952 by Study last updated on 25/Dec/20 $$\underset{{n}=\mathrm{1}} {\overset{\mathrm{10000}} {\sum}}\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)}=??? \\ $$ Commented by Study last updated on 25/Dec/20 $${help}\:{me} \\ $$ Answered…
Question Number 126950 by AST last updated on 05/Dec/22 Answered by floor(10²Eta[1]) last updated on 25/Dec/20 $$\mathrm{A}.\mathrm{1}+\mathrm{2}^{\mathrm{2}^{\mathrm{n}} } +\mathrm{2}^{\mathrm{2}^{\mathrm{n}+\mathrm{1}} } \equiv\mathrm{1}+\left(−\mathrm{1}\right)^{\mathrm{2}^{\mathrm{n}} } +\left(−\mathrm{1}\right)^{\mathrm{2}^{\mathrm{n}+\mathrm{1}} } \equiv\mathrm{1}+\mathrm{1}+\mathrm{1}\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{3}\right)…
Question Number 61412 by Tawa1 last updated on 02/Jun/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{multinomial}\:\mathrm{coefficient}:\:\:\:\:\:\begin{pmatrix}{\:\:\:\:\:\:\:\:\:\mathrm{9}}\\{\mathrm{3},\:\:\mathrm{5},\:\:\mathrm{1},\:\:\mathrm{0}}\end{pmatrix} \\ $$ Commented by mr W last updated on 02/Jun/19 Commented by mr W last…
Question Number 192481 by Tomal last updated on 19/May/23 Answered by aleks041103 last updated on 19/May/23 $$\frac{\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{1}+{x}}\left(\mathrm{1}+\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\right)^{\mathrm{4}} +…\right) \\ $$$${if}\:\:\mid\frac{\mathrm{1}}{\mathrm{1}+{x}}\mid<\mathrm{1},\:{i}.{e}.\:\mid\mathrm{1}+{x}\mid>\mathrm{1} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{1}+{x}}\:\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }}=\frac{\mathrm{1}+{x}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} −\mathrm{1}}…
Question Number 61408 by aliesam last updated on 02/Jun/19 $$\int_{\mathrm{0}} ^{\pi} \frac{{x}}{{tan}^{\mathrm{2}} \left({x}\right)−\mathrm{1}}\:{dx} \\ $$ Answered by tanmay last updated on 02/Jun/19 $$\int_{\mathrm{0}} ^{\pi} \frac{\pi−{x}}{{tan}^{\mathrm{2}}…
Question Number 192477 by Shrinava last updated on 19/May/23 $$\mathrm{Find}:\:\:\:\:\:\frac{\frac{\mathrm{25}}{\mathrm{42}}\:−\:\frac{\mathrm{5}}{\mathrm{16}}\:+\:\frac{\mathrm{10}}{\mathrm{9}}\:−\:\frac{\mathrm{2}}{\mathrm{3}}}{\frac{\mathrm{3}}{\mathrm{8}}\:+\:\frac{\mathrm{4}}{\mathrm{5}}\:−\:\frac{\mathrm{5}}{\mathrm{7}}\:−\:\frac{\mathrm{4}}{\mathrm{3}}}\:=\:? \\ $$ Answered by Tomal last updated on 19/May/23 $$=\frac{\left(\frac{\mathrm{25}}{\mathrm{42}}−\frac{\mathrm{5}}{\mathrm{16}}\right)+\left(\frac{\mathrm{10}}{\mathrm{9}}−\frac{\mathrm{2}}{\mathrm{3}}\right)}{\left(\frac{\mathrm{315}+\mathrm{672}−\mathrm{600}−\mathrm{1120}}{\mathrm{840}}\right)} \\ $$$$=\frac{\left(\frac{\mathrm{200}−\mathrm{105}}{\mathrm{336}}\right)+\left(\frac{\mathrm{10}−\mathrm{6}}{\mathrm{9}}\right)}{−\frac{\mathrm{733}}{\mathrm{840}}} \\ $$$$=\frac{\frac{\mathrm{95}}{\mathrm{336}}+\frac{\mathrm{4}}{\mathrm{9}}}{−\frac{\mathrm{733}}{\mathrm{840}}} \\…