Question Number 138580 by Bekzod Jumayev last updated on 15/Apr/21 Commented by Bekzod Jumayev last updated on 15/Apr/21 $${Please}\:{help}? \\ $$$$ \\ $$ Answered by…
Question Number 73047 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{Z}^{\mathrm{3}} \:\:\:\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}\:} =\mathrm{2}{xyz} \\ $$ Answered by mind is power last updated…
Question Number 73044 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} =\left({n}+\mathrm{1}\right){H}_{{n}} −{n} \\ $$$${and}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} ^{\mathrm{2}} \:=\left({n}+\mathrm{1}\right){H}_{{n}} ^{\mathrm{2}} \:−\left(\mathrm{2}{n}+\mathrm{1}\right){H}_{{n}} \:+\mathrm{2}{n}…
Question Number 73045 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{{C}_{{n}} ^{{k}} }{{C}_{\mathrm{2}{n}−\mathrm{1}} ^{{k}} } \\ $$ Terms of Service Privacy Policy…
Question Number 73042 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:{for}\:\left({n},{p}\right)\in{N}^{\bigstar^{\mathrm{2}} } \:\:\:\sum_{{k}=\mathrm{0}} ^{{p}\:} \:{k}\:{C}_{{n}} ^{{p}−{k}} \:{C}_{{n}} ^{{k}} \:={n}\:{C}_{\mathrm{2}{n}−\mathrm{1}} ^{{p}−\mathrm{1}} \\ $$$${conclude}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:\left({C}_{{n}}…
Question Number 7507 by Master Moon last updated on 01/Sep/16 $$\boldsymbol{{Given}}\:\boldsymbol{{r}},\:\boldsymbol{{t}},\:\boldsymbol{{j}}\:>\mathrm{0}\:\boldsymbol{{and}}\:\boldsymbol{{n}}\geqslant\mathrm{1};\:\boldsymbol{{Prove}}\:\boldsymbol{{that}} \\ $$$$\frac{\left[\underset{\boldsymbol{{p}}_{\mathrm{1}} =\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\left(\boldsymbol{{p}}_{\mathrm{1}} ^{\boldsymbol{{r}}} +\boldsymbol{{r}}\right)+\underset{\boldsymbol{{p}}_{\mathrm{2}} =\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\left(\boldsymbol{{p}}_{\mathrm{2}} ^{\boldsymbol{{t}}} +\boldsymbol{{t}}\right)\right]^{\mathrm{2}} }{\boldsymbol{{n}}^{\mathrm{2}} \left[\left(\boldsymbol{{n}}!\right)^{\frac{\boldsymbol{{r}}+\boldsymbol{{t}}}{\boldsymbol{{n}}}}…
Question Number 138576 by liberty last updated on 15/Apr/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{cot}\:\mathrm{2}{x}\right)^{\mathrm{2tan}\:\mathrm{2}{x}} \:=?\: \\ $$ Answered by phanphuoc last updated on 15/Apr/21 $${li}\underset{{u}\left({x}\right)−>\mathrm{0}} {{m}}\left(\mathrm{1}+{u}\left({x}\right)\right)^{\mathrm{1}/{u}\left({x}\right)} ={e} \\…
Question Number 73043 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} }{{k}}×{C}_{{n}} ^{{k}} \\ $$$${H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Commented…
Question Number 7506 by gourav~ last updated on 01/Sep/16 $$\int\left\{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}\right\}^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{{dx}}{{x}}=? \\ $$$$ \\ $$$$ \\ $$ Answered by Yozzia last updated on 01/Sep/16 $${Let}\:{I}=\int\frac{\mathrm{1}}{{x}}\sqrt{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}}{dx}.…
Question Number 138579 by Jamshidbek last updated on 15/Apr/21 Answered by MJS_new last updated on 16/Apr/21 $${x}\approx\mathrm{5}.\mathrm{40343170} \\ $$ Commented by MJS_new last updated on…