Question Number 80036 by jagoll last updated on 30/Jan/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}=\: \\ $$ Commented by john santu last updated on 30/Jan/20 $$\underset{\mathrm{p}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{p}}…
Question Number 14486 by FilupS last updated on 01/Jun/17 $${S}=\mathrm{1}−\mathrm{2}+\mathrm{3}−\mathrm{4}+… \\ $$$$\therefore{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} {n} \\ $$$$\: \\ $$$${S}=\underset{{s}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} {n}^{\mathrm{1}−{s}} \right) \\…
Question Number 145474 by Ppmaurya last updated on 05/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{R}\:\mathrm{C}\:\mathrm{Classes}\: \\ $$$$\:\:\mathrm{M}.\mathrm{M}.−\mathrm{30}\:\:\:\:\mathrm{10th}−\mathrm{Maths}\:\mathrm{Test}\:\:\:\mathrm{Time}\:\mathrm{Duration}:\mathrm{40min}. \\ $$$$\:\:\mathrm{If}\:\:\mathrm{the}\:\:\mathrm{given}\:\mathrm{expression}\:\mathrm{is}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{then} \\ $$$$\:\mathrm{write}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{and}\:\mathrm{write}\:\:\:\mathrm{three}\:\mathrm{more}\:\mathrm{terms} \\ $$$$\left.\:\:\:\mathrm{Q}.\mathrm{1}\right)\:\:\mathrm{3},\:\mathrm{3}+\sqrt{\mathrm{2},}\:\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}},\:\mathrm{3}+\mathrm{3}\sqrt{\mathrm{2}}…….. \\ $$$$\: \\ $$$$\left.\:\:\mathrm{Q}.\mathrm{2}\right)\:\:\sqrt{\mathrm{2}},\:\sqrt{\mathrm{8}}\:,\sqrt{\mathrm{18}},\sqrt{\mathrm{32}},…… \\ $$$$\left.\:\:\mathrm{Q}.\mathrm{3}\right)\:\:\mathrm{Derive}\:\mathrm{the}\:\mathrm{formula}\:\:\mathrm{a}_{\mathrm{n}} =\:\mathrm{a}+\left(\mathrm{n}−\mathrm{1}\right)\mathrm{d}…
Question Number 79866 by 09264910412 last updated on 28/Jan/20 $${Chapter}\:\left(\mathrm{2}\right) \\ $$$${Remainder}\:{Theorem} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{and} \\ $$$${Factor}\:{Theorem} \\ $$$${Exercises}\left(\mathrm{2}.\mathrm{1}\right) \\ $$$$\boldsymbol{\mathrm{Remainder}}\:\mathrm{T}\boldsymbol{\mathrm{hrorem}} \\ $$$$\mathrm{1}.\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\boldsymbol{\mathrm{x}}^{\mathrm{8}\:} +\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{5} \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{1}\right).…
Question Number 145286 by physicstutes last updated on 03/Jul/21 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{function} \\ $$$$\:{f}\left({x}\right)\:=\sqrt[{\mathrm{3}}]{\mathrm{6}{x}^{\mathrm{2}} −{x}^{\mathrm{3}} } \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{oblique}\:\mathrm{assymptote}\left(\mathrm{s}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}. \\ $$ Answered by Olaf_Thorendsen last updated on 04/Jul/21…
Question Number 145273 by ArielVyny last updated on 03/Jul/21 $${show}\:{that}\:\forall{x}\in\mathbb{R}\:{x}−\mathrm{1}\leqslant{E}\left({x}\right)\leqslant{x} \\ $$ Answered by mathmax by abdo last updated on 04/Jul/21 $$\mathrm{we}\:\mathrm{have}\:\left[\mathrm{x}\right]\leqslant\mathrm{x}<\left[\mathrm{x}\right]+\mathrm{1}\:\Rightarrow\left[\mathrm{x}\right]\leqslant\mathrm{x}\:\mathrm{and}\:\mathrm{x}−\mathrm{1}<\left[\mathrm{x}\right]\:\Rightarrow \\ $$$$\mathrm{x}−\mathrm{1}<\left[\mathrm{x}\right]\leqslant\mathrm{x} \\…
Question Number 79719 by Ell Tee last updated on 27/Jan/20 $$\frac{\left(\mathrm{2}.\mathrm{39}\overset{\mathrm{2}} {\right)}−\left(\mathrm{1}.\mathrm{61}\overset{\mathrm{2}} {\right)}}{\mathrm{2}.\mathrm{39}−\mathrm{1}.\mathrm{61}}…? \\ $$$$ \\ $$ Commented by MJS last updated on 27/Jan/20 $$\frac{{a}^{\mathrm{2}}…
Question Number 145190 by qaz last updated on 03/Jul/21 $$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{x}}\right)=\mathrm{tan}^{−\mathrm{1}} \mathrm{x},\left(\mathrm{x}\neq\mathrm{0}\right) \\ $$$$\mathrm{Find}\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Answered by EDWIN88 last updated on 03/Jul/21 $$\left(\mathrm{1}\right){f}\left({x}\right)+{f}\left(\frac{{x}−\mathrm{1}}{{x}}\right)=\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right) \\…
Question Number 79647 by john santu last updated on 27/Jan/20 $$\mathrm{discussion}\:\mathrm{back}\:\mathrm{with}\:\mathrm{mr}\:\mathrm{W}. \\ $$$$\mathrm{consider}\:\mathrm{this}\:\mathrm{equation}\: \\ $$$$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}\right)\left(\mathrm{3}^{\mathrm{x}} −\mathrm{27}\right)=\mathrm{0} \\ $$$$\mathrm{does}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{have}\:\mathrm{two}\:\mathrm{roots} \\ $$$$\mathrm{or}\:\mathrm{three}\:\mathrm{roots}? \\ $$ Commented by…
Question Number 79625 by M±th+et£s last updated on 26/Jan/20 $${if}\:{n}>\mathrm{1}\:{prove}\:{that} \\ $$$$\mathrm{2}{ln}\left({n}\right)−{ln}\left({n}+\mathrm{1}\right)−{ln}\left({n}−\mathrm{1}\right)=\frac{\mathrm{1}}{{n}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{3}{n}^{\mathrm{6}} }+…= \\ $$ Answered by mind is power last updated on…