Category: Algebra

Question Number 118790 by mathocean1 last updated on 19/Oct/20 $$\mathrm{Show}\mathrm{by}\mathrm{recurence}\mathrm{that}$$$${(\mathrm{a}+\mathrm{b})}^{\mathrm{n}}=\underset{\mathrm{k}=0}{\sum ^{\mathrm{n}}}{\mathrm{C}}_{\mathrm{n}}^{\mathrm{k}}\times {\mathrm{a}}^{\mathrm{k}}\times {\mathrm{b}}^{\mathrm{n}-\mathrm{k}}$$ Terms of Service Privacy Policy…

Question Number 118775 by obaidullah last updated on 19/Oct/20 $$2,2,2,2,2$$$$X=\frac{2+2+2+2+2}{5}=\frac{10}{5}=2$$$$V=\frac{{(2-2)}^2+{(2-2)}^2+{(2-2)}^2+{(2-2)}^2+{(2-2)}^2}{5}$$$$Variance=0$$ Terms of…

Question Number 184305 by HeferH last updated on 05/Jan/23 $$if:f\left(x\right)=x^2+2x$$$$findx:$$$$f\left(f\left(f(x+2)\right)\right)=99999999$$ Answered by Frix last updated on 05/Jan/23 $${x}={t}−\mathrm{3}…

Question Number 118770 by obaidullah last updated on 19/Oct/20 $$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{n!}{n^n}\right)}^{\frac{1}{n}}=?$$$$y={\left(\frac{n!}{n^n}\right)}^{\frac{1}{n}}=\frac{1}{n}ln\left(\frac{n!}{n^n}\right)=\frac{1}{n}[lnn!-nlnn]$$$$\Rightarrow \underset{x\to \mathrm{\infty }}{\lim }lny=\underset{x\to \mathrm{\infty }}{\lim }\frac{1}{n}[nlnn-n-nlnn]$$$$\Rightarrow{ln}\underset{{x}\rightarrow\infty} {\mathrm{lim}}{y}=\underset{{x}\rightarrow\infty}…

Question Number 184280 by mr W last updated on 04/Jan/23 $$Given\{\begin{array}{l}{a}_0=1\\ a_{n+1}=\frac{1}{2}(3a_n+\sqrt{5a_n^2-4})\end{array}$$$$\mathrm{\forall }n⩾0,n\in I$$$$find{a}_n.$$ Commented by…