Menu Close

Author: Tinku Tara

factorise-x-3-1-

Question Number 10572 by j.masanja06@gmail.com last updated on 18/Feb/17 $$\mathrm{factorise} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1} \\ $$ Answered by sandy_suhendra last updated on 18/Feb/17 $$=\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right) \\…

Question-141640

Question Number 141640 by Willson last updated on 21/May/21 Answered by qaz last updated on 22/May/21 $$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{16}^{{k}} \left(\mathrm{8}{k}+{n}\right)} \\ $$$$=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{16}^{{k}} }\int_{\mathrm{0}}…

Question-141643

Question Number 141643 by Gbenga last updated on 21/May/21 Answered by qaz last updated on 22/May/21 $${S}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{5}{n}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{16}^{{n}} } \\ $$$$=\left(\mathrm{5}{xD}+\mathrm{1}\right)^{\mathrm{2}} \mid_{{x}=\mathrm{1}/\mathrm{16}} \underset{{n}=\mathrm{0}}…

Question-10566

Question Number 10566 by krist last updated on 18/Feb/17 Answered by ridwan balatif last updated on 18/Feb/17 $$\int\frac{\mathrm{cos}{x}}{\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int\frac{\mathrm{cos}{x}}{\mathrm{sin}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int\frac{\mathrm{cos}{x}}{\mathrm{sin}{x}}×\frac{\mathrm{1}}{\mathrm{sin}{x}}{dx} \\…

1-lt-a-lt-b-prove-that-b-n-k-0-n-1-k-C-n-k-a-ln-p-0-n-k-C-n-k-p-a-n-p-b-p-ln-a-

Question Number 141633 by Willson last updated on 21/May/21 $$\mathrm{1}<\mathrm{a}<\mathrm{b}\:,\mathrm{prove}\:\mathrm{that}\:: \\ $$$${b}^{{n}} \:=\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \mathrm{C}_{{n}} ^{{k}} \:{a}^{\frac{{ln}\left(\underset{{p}=\mathrm{0}} {\overset{{n}−{k}} {\sum}}\mathrm{C}_{{n}−{k}} ^{{p}} {a}^{{n}−{p}} {b}^{{p}} \right)}{{ln}\left({a}\right)}} \\…

Question-76098

Question Number 76098 by vishalbhardwaj last updated on 23/Dec/19 Answered by benjo last updated on 23/Dec/19 $$\mathrm{5}.\:\mathrm{let}\:\mathrm{x}\:=\:\mathrm{u}\:+\:\mathrm{c}\:\Rightarrow\mathrm{dx}\:=\mathrm{du}\: \\ $$$$\mathrm{so}\:\mathrm{we}\:\mathrm{have}\:\overset{\mathrm{b}} {\int}\mathrm{f}\left(\mathrm{u}+\mathrm{c}\right)\mathrm{du}\: \\ $$ Commented by john…