Question Number 158483 by HongKing last updated on 04/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158465 by HongKing last updated on 04/Nov/21 Answered by qaz last updated on 04/Nov/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\begin{pmatrix}{\mathrm{2n}}\\{\:\:\mathrm{n}}\end{pmatrix}}{\mathrm{4}^{\mathrm{n}} \left(\mathrm{4n}+\mathrm{5}\right)\left(\mathrm{2n}+\mathrm{2}\right)} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{−\mathrm{1}/\mathrm{2}}\\{\:\:\:\:\:\mathrm{n}}\end{pmatrix}\left(−\mathrm{1}\right)^{\mathrm{n}} \left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}−\frac{\mathrm{4}}{\mathrm{4n}+\mathrm{5}}\right)…
Question Number 27384 by abdo imad last updated on 05/Jan/18 $${let}\:{give}\:\:{p}\left({x}\right)=\:\left(\frac{\mathrm{1}+{ix}}{\mathrm{1}−{ix}}\right)^{{n}} −\:\frac{\mathrm{1}+{itan}\alpha\:}{\mathrm{1}−{itan}\alpha}\:\:{factorize}\:{p}\left({x}\right)\:{inside} \\ $$$${C}\left[{x}\right]. \\ $$ Commented by abdo imad last updated on 07/Jan/18 $${roots}\:{of}\:{p}\left({x}\right)\:\:…
Question Number 27382 by abdo imad last updated on 05/Jan/18 $${resolve}\:{inside}\:{C}\:\:\left(\frac{{z}−{i}}{{z}+{i}}\right)^{{n}} +\left(\frac{{z}+{i}}{{z}−{i}}\right)^{{n}} =\:\mathrm{2}{cos}\theta\:{and}\mathrm{0}\:<\theta<\pi\:.{n}\:{integer}. \\ $$ Answered by sma3l2996 last updated on 05/Jan/18 $$\left(\frac{{z}−{i}}{{z}+{i}}\right)^{{n}} +\left(\frac{{z}−{i}}{{z}+{i}}\right)^{−{n}} −\mathrm{2}{cos}\theta=\mathrm{0}…
Question Number 158455 by mnjuly1970 last updated on 04/Nov/21 Answered by MJS_new last updated on 05/Nov/21 $$\sqrt{{x}\lfloor{x}\rfloor+{x}^{\mathrm{2}} \lfloor{x}−\mathrm{1}\rfloor}=\sqrt{{x}\left(\left({x}+\mathrm{1}\right)\lfloor{x}\rfloor−{x}\right)} \\ $$$${g}\left({x}\right)={x}\left(\left({x}+\mathrm{1}\right)\lfloor{x}\rfloor−{x}\right)=\mathrm{0}\:\Leftrightarrow\:{x}=\mathrm{0}\vee\left({x}+\mathrm{1}\right)\lfloor{x}\rfloor={x} \\ $$$$\Rightarrow\:{x}=\mathrm{0}\vee{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{but}\:\left(\underset{{x}\rightarrow\mathrm{1}^{−} }…
Question Number 27376 by macanudo last updated on 05/Jan/18 Commented by prakash jain last updated on 05/Jan/18 $$\mathrm{S}=\underset{{k}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} {x}^{{k}} \\ $$$${S}=\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}}…
Question Number 158444 by HongKing last updated on 04/Nov/21 $$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{with} \\ $$$$\frac{\mathrm{2010}}{\mathrm{2011}}\:<\:\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{y}}}\:<\:\frac{\mathrm{2011}}{\mathrm{2012}}\:\:\mathrm{then}\:\mathrm{compute}\:\mathrm{the} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{for}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{values}\:\mathrm{of}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{which}\:\mathrm{achieves} \\ $$$$\mathrm{this}\:\mathrm{minimum} \\ $$ Commented by mr W last…
Question Number 158443 by HongKing last updated on 04/Nov/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{divisors}\:\mathrm{has}\:\mathrm{the}\:\mathrm{positive} \\ $$$$\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{which}\:\mathrm{verify} \\ $$$$\mathrm{n}^{\boldsymbol{\mathrm{n}}} \:=\:\mathrm{2027}^{\mathrm{2027}^{\mathrm{2028}} } \:? \\ $$ Answered by MJS_new last updated on…
Question Number 158438 by amin96 last updated on 04/Nov/21 Commented by amin96 last updated on 04/Nov/21 $$ \\ $$ Given the values of x and…
Question Number 92899 by gonzo last updated on 09/May/20 $${y}=−\mathrm{2}.\mathrm{241}{x}+\mathrm{1}.\mathrm{585} \\ $$$${how}\:{do}\:{i}\:{find}\:{value}\:{of}\:{x}\:{by}\:{rearranging} \\ $$ Commented by mr W last updated on 09/May/20 $${x}=\frac{\mathrm{1}.\mathrm{585}−{y}}{\mathrm{2}.\mathrm{241}} \\ $$…