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prove-k-1-n-k-k-1-k-k-1-k-2-3-

Question Number 8988 by Daily last updated on 10/Nov/16 $${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}\left({k}+\mathrm{1}\right)={k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)/\mathrm{3} \\ $$ Answered by 123456 last updated on 11/Nov/16 $${s}\left({n}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}}…

Question-74527

Question Number 74527 by Maclaurin Stickker last updated on 25/Nov/19 Commented by Maclaurin Stickker last updated on 25/Nov/19 $${In}\:{the}\:{figure}\:{determine}\:{the}\:{radius} \\ $$$${of}\:{the}\:{smallest}\:{circumference}\:{as}\:{a} \\ $$$${function}\:{of}\:{the}\:{radius}\:\boldsymbol{\mathrm{R}}\:{of}\:{the}\:{quadrant}. \\ $$…

ls-

Question Number 8969 by lsaBELA last updated on 08/Nov/16 $${ls} \\ $$ Commented by 123456 last updated on 08/Nov/16 $$\mathrm{R}^{\mathrm{3}} \\ $$$${m}=\left\{\right\} \\ $$$$\mathrm{1}\leqslant{i}\leqslant{a};{m}\left[{i}\right]=\left\{\right\} \\…

Question-74503

Question Number 74503 by crystal0207 last updated on 25/Nov/19 Commented by mathmax by abdo last updated on 25/Nov/19 $$\left.{a}\right)\int_{\mathrm{0}} ^{\infty} \:{x}^{\alpha−\mathrm{1}} \:{e}^{−\lambda{x}} {dx}\:=_{\lambda{x}={t}} \:\:\:\:\int_{\mathrm{0}} ^{\infty}…

Prove-that-1-1-2-1-3-1-2009-2009-1-2-2-3-3-4-2008-2009-

Question Number 8958 by Sopheak last updated on 07/Nov/16 $${Prove}\:{that}\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+….+\frac{\mathrm{1}}{\mathrm{2009}}=\mathrm{2009}−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{4}}+…+\frac{\mathrm{2008}}{\mathrm{2009}}\right) \\ $$ Answered by sou1618 last updated on 07/Nov/16 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}…+\frac{\mathrm{1}}{\mathrm{2009}} \\ $$$$=\left(\mathrm{1}−\frac{\mathrm{0}}{\mathrm{1}}\right)+\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\right)+\left(\mathrm{1}−\frac{\mathrm{2}}{\mathrm{3}}\right)+\left(\mathrm{1}−\frac{\mathrm{3}}{\mathrm{4}}\right)…+\left(\mathrm{1}−\frac{\mathrm{2008}}{\mathrm{2009}}\right) \\ $$$$=\mathrm{2009}−\left(\frac{\mathrm{0}}{\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{4}}…+\frac{\mathrm{2008}}{\mathrm{2009}}\right) \\…

Let-n-be-a-positive-integer-such-that-one-of-the-roofs-of-the-quadratic-equation-4x-2-4-3-4-x-3-n-24-0-is-an-integer-Find-the-value-of-n-

Question Number 8957 by Sopheak last updated on 07/Nov/16 $$\: \\ $$$${Let}\:{n}\:{be}\:{a}\:{positive}\:{integer}\:{such}\:{that}\:{one}\:{of} \\ $$$${the}\:{roofs}\:{of}\:{the}\:{quadratic}\:{equation}\: \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\left(\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{4}\right){x}+\sqrt{\mathrm{3}}{n}−\mathrm{24}=\mathrm{0}\:{is}\:{an}\:{integer}\: \\ $$$${Find}\:{the}\:{value}\:{of}\:{n}\: \\ $$$$\: \\ $$ Commented by…

Question-74483

Question Number 74483 by liki last updated on 24/Nov/19 Commented by liki last updated on 24/Nov/19 $$…\:{sory}\:{mr}\:{w},{i}\:{tried}\:{to}\:{this}\:{qns}\:{according} \\ $$$$\:{to}\:{your}\:{idea}\:{but}\:{i}\:{didn}'{t}\:{get}\:{the}\:{answer}\:{so}\: \\ $$$$\:{plz}\:{assist}\:{me}! \\ $$ Commented by…