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Question Number 100618 by bachamohamed last updated on 27/Jun/20 $$\:\:\:\:\:\:\:\:\:\:\:\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{k}}=\boldsymbol{{n}}} {\sum}}\:\frac{\boldsymbol{{ln}}\left(\boldsymbol{{k}}\right)}{\mathrm{2}^{\boldsymbol{{k}}} }\:=? \\ $$ Answered by maths mind last updated on 28/Jun/20 $${this}\:{quation}\:{i}\:{see}\:{it}\:{many}\:{Times}\: \\…
Question Number 100614 by bachamohamed last updated on 27/Jun/20 $$\:\:\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{k}}=\boldsymbol{{n}}−\mathrm{1}} {\sum}}\frac{\boldsymbol{{ln}}\left(\boldsymbol{{k}}!\right)}{\mathrm{2}^{\boldsymbol{{k}}+\mathrm{1}} }\:=?\:\:\:\: \\ $$$$\:\:\boldsymbol{\mathrm{A}{ny}}\:\boldsymbol{{help}}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 166141 by Lambert last updated on 13/Feb/22 $$\int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \frac{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }{\:\sqrt{\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\: \\ $$ Answered by MJS_new last updated on 14/Feb/22 $$\int\frac{{t}^{\mathrm{2}} }{\:\sqrt{{a}+\mathrm{2}{t}^{\mathrm{2}}…
Question Number 166135 by mkam last updated on 13/Feb/22 $${find}\:{the}\:{domain}\:{of}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left[{x}\right]−\mathrm{1}} \\ $$ Commented by mkam last updated on 13/Feb/22 $$????? \\ $$ Answered by Mathspace…
Question Number 166111 by DAVONG last updated on 13/Feb/22 Answered by qaz last updated on 13/Feb/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \mathrm{sin}\:\mathrm{x}−\mathrm{x}\left(\mathrm{1}+\frac{\mathrm{5}}{\mathrm{6}}\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{5}} } \\ $$$$=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}}…
Question Number 100575 by bshahid010@gmail.com last updated on 27/Jun/20 Answered by Ar Brandon last updated on 27/Jun/20 $$\mathrm{Let}\:\mathcal{I}=\underset{\mathrm{x}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \mathrm{dx}=\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{\mathrm{x}^{\mathrm{2}}…
Question Number 166110 by naka3546 last updated on 13/Feb/22 $$\mathrm{Prove}\:\:\mathrm{that} \\ $$$$\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{0}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{1}}\end{pmatrix}^{\mathrm{2}} \:+\:\begin{pmatrix}{\:{n}}\\{\:\mathrm{2}}\end{pmatrix}^{\mathrm{2}} \:+\:\ldots+\:\begin{pmatrix}{\:{n}}\\{\:{n}}\end{pmatrix}^{\mathrm{2}} \:\:=\:\:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix} \\ $$ Answered by qaz last updated on 13/Feb/22…
Question Number 100570 by bshahid010@gmail.com last updated on 27/Jun/20 Commented by Dwaipayan Shikari last updated on 27/Jun/20 $${a}^{{x}} ={b}^{{y}} ={c}^{{z}} ={d}^{{w}} ={k}\:\:\left({k}\neq\mathrm{0}\right) \\ $$$${a}={k}^{\frac{\mathrm{1}}{{x}}} \:\:{b}={k}^{\frac{\mathrm{1}}{{y}}}…