Category: Algebra

Question Number 79946 by mr W last updated on 29/Jan/20 $${Find}\: \\ $$$$\int_{\mathrm{0}} ^{\:{n}} \left[\sqrt[{\mathrm{3}}]{{x}}\right]{dx}=?\: \\ $$$${in}\:{terms}\:{of}\:{n}.\:\left({n}\in\mathbb{N}\right) \\ $$ Answered by key of knowledge last…

Question Number 14398 by tawa tawa last updated on 31/May/17 $$\mathrm{Solve}:\: \\ $$$$\frac{\mathrm{7}}{\mathrm{2}}\:+\:\frac{\mathrm{3y}}{\mathrm{x}\:+\:\mathrm{y}}\:=\:\sqrt{\mathrm{x}}\:+\:\mathrm{4}\sqrt{\mathrm{y}}\:\:\:\:\:\:\:\:\:\:\:\:……….\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\left(\mathrm{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{4}\:+\:\mathrm{2xy}\left(\mathrm{x}\:−\:\mathrm{1}\right)\:\:\:\:……….\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on…

Question Number 145459 by syamilkamil1 last updated on 05/Jul/21 $${prove}\:\left({A}\:−\:{B}\right)−{C}\:=\:{A}\:−\left({B}\:\cup\:{C}\right) \\ $$ Answered by liberty last updated on 05/Jul/21 $$\:{A}−{B}={A}\cap{B}^{{c}} \\ $$$$\Rightarrow\left({A}−{B}\right)−{C}\:=\:\left({A}\cap{B}^{{c}} \right)\cap{C}^{{c}} \: \\…

Question Number 145444 by mathdanisur last updated on 04/Jul/21 $$\frac{\mathrm{1}}{\mathrm{2}}\:-\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{7}}{\mathrm{8}}\:-\:\frac{\mathrm{15}}{\mathrm{16}}\:+\:…\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\mathrm{S}\:=\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \frac{\mathrm{2}^{{n}+\mathrm{1}} −\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }…

Question Number 145436 by mathdanisur last updated on 04/Jul/21 Commented by justtry last updated on 05/Jul/21 Commented by mathdanisur last updated on 05/Jul/21 $${thanks}\:{Ser},\:{but}\:{wrong} \\…