Question Number 192425 by mehdee42 last updated on 17/May/23 $${Question} \\ $$$${if}\:\:“{k}''\:{is}\:{odd}\:\:\&\:{A}=\mathrm{1}^{{k}} +\mathrm{2}^{{k}} +…+{n}^{{k}\:\:} \:\&\:\:{B}=\mathrm{1}+\mathrm{2}+…+{n} \\ $$$${prove}\:{that}\:\::\:\:{B}\:\mid\:{A}\: \\ $$ Answered by MM42 last updated on…
Question Number 192426 by mathlove last updated on 17/May/23 $${log}\left(−\mathrm{10}\right)\left(−\mathrm{10}\right)=? \\ $$ Answered by Frix last updated on 18/May/23 $$\mathrm{Unclear}: \\ $$$$\mathrm{log}\:\left({a}\right)\:\left({a}\right)\:=\left({a}\right)\mathrm{log}\:\left({a}\right) \\ $$$$−\mathrm{10}\:\mathrm{log}\:\left(−\mathrm{10}\right)\:=−\mathrm{10log}\:\left(\mathrm{10e}^{\mathrm{i}\pi} \right)…
Question Number 126886 by SOMEDAVONG last updated on 25/Dec/20 $$\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}\:+….+\:\frac{\mathrm{1}}{\mathrm{2n}}\right) \\ $$ Answered by Dwaipayan Shikari last updated on 25/Dec/20 $$\frac{\mathrm{1}}{{n}}\left(\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{{n}}}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{2}}{{n}}}+….+\frac{\mathrm{1}}{\mathrm{1}+\frac{{n}}{{n}}}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{1}+\frac{{r}}{{n}}}…
Question Number 192420 by Mingma last updated on 17/May/23 Commented by AST last updated on 18/May/23 $${Q}\mathrm{191758} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 126887 by mnjuly1970 last updated on 25/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{calculus}… \\ $$$${please}\:\:{solve}:\:\left(\:{with}\:{explanation}\right) \\ $$$$\:\:\:\:\left\{_{{x}^{\mathrm{2}} +{y}=\mathrm{3}} ^{{x}+{y}^{\mathrm{2}} =\mathrm{5}} \right. \\ $$$$ \\ $$ Commented by Lordose…
Question Number 61349 by tanmay last updated on 01/Jun/19 Commented by MJS last updated on 01/Jun/19 $$…\mathrm{harder}\:\mathrm{than}\:\mathrm{I}\:\mathrm{thought} \\ $$$$\int\frac{\sqrt{{t}^{\mathrm{2}} −\mathrm{5}}}{{t}−{a}}{dt}= \\ $$$$\:\:\:\:\left[{t}=\frac{\sqrt{\mathrm{5}}}{\mathrm{sin}\:{u}}\:\Leftrightarrow\:{u}=\mathrm{arcsin}\:\frac{\sqrt{\mathrm{5}}}{{t}}\:\rightarrow\:{dt}=−\frac{{t}\sqrt{{t}^{\mathrm{2}} −\mathrm{5}}}{\:\sqrt{\mathrm{5}}}{du}\right] \\ $$$$\:\:\:\:\:\mathrm{now}\:\mathrm{the}\:\mathrm{root}\:\mathrm{is}\:\mathrm{gone},\:\mathrm{but}\:\mathrm{we}\:\mathrm{must}\:\mathrm{make}…
Question Number 126882 by Mathgreat last updated on 25/Dec/20 $$\boldsymbol{{x}}^{\boldsymbol{{x}}} =\mathrm{3} \\ $$ Answered by Lordose last updated on 25/Dec/20 $$\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{3}\:\left\{\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{e}^{\mathrm{xln}\left(\mathrm{x}\right)} \right\} \\…
Question Number 61347 by Tawa1 last updated on 01/Jun/19 Commented by mr W last updated on 02/Jun/19 $${x}=\mathrm{20}°,\:{see}\:{also}\:{Q}\mathrm{43728}. \\ $$ Answered by peter frank last…
Question Number 61343 by bhanukumarb2@gmail.com last updated on 01/Jun/19 Answered by MJS last updated on 01/Jun/19 $${x}={a}−\frac{\mathrm{1}}{{a}−\frac{\mathrm{1}}{{a}−…}} \\ $$$${x}={a}−\frac{\mathrm{1}}{{x}} \\ $$$${x}^{\mathrm{2}} −{ax}+\mathrm{1}=\mathrm{0} \\ $$$${x}=\frac{{a}}{\mathrm{2}}\pm\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{4}}}{\mathrm{2}}…
Question Number 126879 by bramlexs22 last updated on 25/Dec/20 $$\:\int\:\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:? \\ $$ Answered by Lordose last updated on 25/Dec/20 $$\Omega\:=\:\int^{\:} \frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{1}+\mathrm{x}^{\mathrm{8}} }\mathrm{dx}\:=\:\underset{\mathrm{n}=\mathrm{0}}…