Category: Relation and Functions

Question Number 57408 by Abdo msup. last updated on 03/Apr/19 $$letthesequence\left(a_n\right)wichverify{a}_1=2and$$$$a_{n+1}=a_n+\sqrt{1+\frac{a_n}{n}}$$$$provethat{\left(\frac{a_n}{n}\right)}_{n⩾1}isconvergente.$$ Terms…

Question Number 57407 by Abdo msup. last updated on 03/Apr/19 $$let{U}_0=cos\left(\frac{\pi }{3}\right)and{U}_{n+1}=\sqrt{\frac{1+U_n}{2}}$$$$find{U}_{n}intermsofn.$$ Commented by Abdo msup. last updated…

Question Number 122788 by 676597498 last updated on 19/Nov/20 Answered by mr W last updated on 20/Nov/20 $$0<\frac{1}{2}+\frac{1}{1000}<1\Rightarrow [\frac{1}{2}+\frac{1}{1000}]=0$$$$\dots$$$$0<\frac{1}{2}+\frac{499}{1000}<1\Rightarrow [\frac{1}{2}+\frac{499}{1000}]=0$$$$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{500}}{\mathrm{1000}}=\mathrm{1}\Rightarrow\left[\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{500}}{\mathrm{1000}}\right]=\mathrm{1} \…

Question Number 122615 by john santu last updated on 18/Nov/20 Commented by liberty last updated on 18/Nov/20 $$\frac{1}{t}=\frac{1}{12}+\frac{1}{15}-\frac{1}{10}=\frac{5+4-6}{60}$$$$\frac{1}{t}=\frac{1}{20}\Rightarrow t=20hours$$ Terms of Service…

Question Number 57010 by 121194 last updated on 28/Mar/19 $$f\left(\frac{x+y}{2}\right)=\frac{f\left(x\right)f\left(y\right)}{f\left(2\right)}$$$$f\left(x\right)=?$$ Commented by maxmathsup by imad last updated on 29/Mar/19 $${x}={y}\:\Rightarrow{f}\left({x}\right)=\frac{{f}^{\mathrm{2}} \left({x}\right)}{{f}\left(\mathrm{2}\right)}\:\:{with}\:{f}\left(\mathrm{2}\right)\neq\mathrm{0}\:\Rightarrow{f}^{\mathrm{2}}…