Question Number 212326 by universe last updated on 10/Oct/24 $$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{3}\right)^{{n}} \:{n}!}{\mathrm{1}.\mathrm{4}…\left(\mathrm{3}{n}+\mathrm{1}\right)} \\ $$$$\:\left(\mathrm{1}\right)\:{check}\:\:{its}\:{a}\:{absolute}\:{conergent}\:{series} \\ $$$$\:\:\left(\mathrm{2}\right)\:{show}\:{that}\:{its}\:{a}\:{convergent}\:{series} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 212327 by MASANJAJJ last updated on 10/Oct/24 $${if}\:\left({a}+\frac{\mathrm{1}}{{a}}\right)=\mathrm{15}\:{find}\:{the}\:{value}\:{of}\:\left({a}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{a}^{\mathrm{2}} }\right) \\ $$ Answered by universe last updated on 10/Oct/24 $$\left({a}+\frac{\mathrm{1}}{{a}}\right)^{\mathrm{2}} \:=\:\mathrm{15}^{\mathrm{2}} \\ $$$${a}^{\mathrm{2}}…
Question Number 212320 by RojaTaniya last updated on 10/Oct/24 $$\:{a}+{b}+{c}+{d}=\mathrm{2},\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{2} \\ $$$$\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} =−\mathrm{4},\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +{d}^{\mathrm{4}} =−\mathrm{6} \\…
Question Number 212339 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{{x}^{\mathrm{3}/\mathrm{4}} \left(\mathrm{3}−{x}\right)^{\mathrm{1}/\mathrm{4}} }{\left(\mathrm{5}−{x}\right)^{\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\left(\frac{\mathrm{2}{x}}{\mathrm{5}\left(\mathrm{3}−{x}\right)}\right)^{\mathrm{1}/\mathrm{4}} ;\:{C}=\frac{\mathrm{9}\sqrt[{\mathrm{4}}]{\mathrm{2}}}{\mathrm{5}\sqrt[{\mathrm{4}}]{\mathrm{5}}}\right]…
Question Number 212301 by RojaTaniya last updated on 09/Oct/24 $$\:\:\:\:\mathrm{3}{x}+\frac{\mathrm{2}}{\:\sqrt{{x}}}=\mathrm{1},\:{x}−\sqrt{{x}}\:=? \\ $$$$\:\: \\ $$ Answered by Sutrisno last updated on 09/Oct/24 $${misal}\:\sqrt{{x}}={p}\rightarrow{x}={p}^{\mathrm{2}} \\ $$$$\mathrm{3}{p}^{\mathrm{2}} +\frac{\mathrm{2}}{{p}}=\mathrm{1}…
Question Number 212319 by Ghisom last updated on 09/Oct/24 $$\mathrm{find} \\ $$$${G}=\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{sin}\:{x}}\:{dx} \\ $$ Commented by Spillover last updated on 10/Oct/24 $$\frac{\pi}{\mathrm{4}}\mathrm{ln}\:\mathrm{2}\:\:{right}? \\…
Question Number 212314 by Spillover last updated on 09/Oct/24 Answered by mehdee7396 last updated on 09/Oct/24 $${f}\left({x}\right)={ln}\left(\frac{\mathrm{2}−{sinx}}{\mathrm{2}+{sinx}}\right) \\ $$$${f}\left(−{x}\right)={ln}\left(\frac{\mathrm{2}+{sinx}}{\mathrm{2}−{sinx}}\right)=−{f}\left({x}\right) \\ $$$$\Rightarrow;{f};\:{is}\:\:;{odd}\Rightarrow\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} {f}\left({x}\right){dx}=\mathrm{0}\:\checkmark \\ $$$$…
Question Number 212311 by MrGaster last updated on 09/Oct/24 $$ \\ $$$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\:\underset{{j}=\mathrm{1}} {\overset{{n}^{\mathrm{2}} } {\sum}}\:\mathrm{sin}\frac{{k}}{{n}}\centerdot\mathrm{sin}\frac{{k}}{{n}^{\mathrm{2}} }\centerdot\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} +{j}}}\mathrm{l}{n}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right) \\ $$ Terms of Service…
Question Number 212242 by York12 last updated on 08/Oct/24 $$\mathrm{Help} \\ $$ Commented by York12 last updated on 08/Oct/24 Commented by Frix last updated on…
Question Number 212291 by hardmath last updated on 08/Oct/24 Commented by hardmath last updated on 08/Oct/24 $$\mathrm{m}\left(\angle\mathrm{BCD}\right)\:=\:\mathrm{90}° \\ $$$$\mid\mathrm{AB}\mid\:=\:\mid\mathrm{AC}\mid \\ $$$$\mathrm{AC}\:\cap\:\mathrm{BD}\:=\:\mathrm{K} \\ $$$$\mathrm{Area}\left(\mathrm{ABCD}\right)\:=\:? \\ $$…