Question Number 8175 by prakash jain last updated on 02/Oct/16 $$\mathrm{Prove} \\ $$$$\frac{\mathrm{4}^{{n}} }{{n}}<\:^{\mathrm{2}{n}} {C}_{{n}} \:\mathrm{for}\:\mathrm{all}\:{n}\geqslant\mathrm{4}\:\mathrm{and}\:{n}\in\mathbb{Z}^{+} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8168 by aungnaingsoe last updated on 02/Oct/16 $${Find}\:{the}\:{coefficient}\:{of}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)…\left(\mathrm{1}+{x}^{{n}} \right). \\ $$ Commented by Rasheed Soomro last updated on 02/Oct/16…
Question Number 73673 by ajfour last updated on 14/Nov/19 Commented by ajfour last updated on 14/Nov/19 $${Q}\:\mathrm{73503}\:\:\:\left({another}\:{way}\:\:{a}\:{try}..\right) \\ $$ Commented by ajfour last updated on…
Question Number 8129 by Apoorva22 last updated on 01/Oct/16 $${An}\:{ellipse}\:{having}\:{focii}\:{at}\:\left(\mathrm{3}\:\mathrm{3}\right){and}\:\left(−\mathrm{4}\:\mathrm{4}\right)\:{and}\:{passing}\:{through}\:{origin}\:{has}\:{e}?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8127 by Yozzia last updated on 30/Sep/16 $${For}\:\mid{x}\mid<\mathrm{1},\:{we}\:{have}\:{that} \\ $$$$\left(\mathrm{1}+{x}\right)^{\mathrm{1}/\mathrm{2}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{x}+\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{1}\right)}{\mathrm{2}!}{x}^{\mathrm{2}} +\frac{\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{1}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}\right)}{\mathrm{3}!}{x}^{\mathrm{3}} +… \\ $$$$\left(\mathrm{1}+{x}\right)^{\mathrm{1}/\mathrm{2}} =\mathrm{1}+\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\underset{{k}=\mathrm{0}} {\overset{{r}−\mathrm{1}} {\prod}}\left(\mathrm{0}.\mathrm{5}−{k}\right)}{{r}!}{x}^{{r}} . \\ $$$${Let}\:{g}\left({r}\right)=\underset{{k}=\mathrm{0}}…
Question Number 73663 by ajfour last updated on 14/Nov/19 Answered by ajfour last updated on 15/Nov/19 $${See}\:{Q}.\mathrm{73673} \\ $$$${V}=\mathrm{2}\int\left(\left(\frac{\rho^{\mathrm{2}} \left(\mathrm{2}\phi\right)}{\mathrm{2}}×\left(−{ds}\right)\right)\right. \\ $$$$\:\rho={s}\mathrm{sin}\:\alpha={s}\mathrm{sin}\:\frac{\pi}{\mathrm{6}}\:=\:\frac{{s}}{\mathrm{2}} \\ $$$$\:{s}=\frac{{a}\sqrt{\mathrm{3}}−{r}\left(\mathrm{1}−\mathrm{cos}\:\theta\right)}{\mathrm{cos}\:\alpha}=\frac{\mathrm{2}{a}}{\mathrm{3}}\left(\mathrm{2}+\mathrm{cos}\:\theta\right) \\…
Question Number 73620 by L.Messi last updated on 14/Nov/19 Answered by MJS last updated on 14/Nov/19 $$\mathrm{do}\:\mathrm{you}\:\mathrm{at}\:\mathrm{least}\:\mathrm{know}\:\mathrm{what}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{Circle}\:\mathrm{is}, \\ $$$$\mathrm{Sir}\:\mathrm{L}.\:\mathrm{Messi}? \\ $$ Commented by L.Messi last…
Question Number 8035 by Nayon last updated on 28/Sep/16 $${prove}\:>>\:{a}^{{n}} +{b}^{{n}} ={c}^{{n}} \:\:\left[{n}>\mathrm{2}\right] \\ $$$${it}\:{has}\:{no}\:{integer}\:{roots} \\ $$$$ \\ $$ Commented by FilupSmith last updated on…
Question Number 8032 by Nayon last updated on 28/Sep/16 $${find}\:{the}\:{real}\:{root}: \\ $$$$\mathrm{99}{x}^{\mathrm{3}} +\mathrm{297}{x}^{\mathrm{2}} +\mathrm{594}{x}−\mathrm{7867}=\mathrm{0} \\ $$ Answered by prakash jain last updated on 28/Sep/16 $${x}={y}−\mathrm{1}…
Question Number 8031 by Nayon last updated on 28/Sep/16 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{2}}\:\approx\frac{\mathrm{19601}}{\mathrm{13860}} \\ $$ Answered by prakash jain last updated on 28/Sep/16 $$\sqrt{\mathrm{2}}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{2}}}\:\:\:\:…\left({i}\right) \\ $$$$\mathrm{putting}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{2}}\:\mathrm{from}\:\left({i}\right)\:\mathrm{in}\:\mathrm{RHS} \\ $$$$\mathrm{of}\:\left({i}\right)…