Category: Relation and Functions

Question Number 49961 by maxmathsup by imad last updated on 12/Dec/18 $$findthesequence\left(a_n\right)wichverify$$$$\left(\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} \right)\left(\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−{x}\right)^{{n}} }{{n}+\mathrm{1}}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:{a}_{{n}} {x}^{{n}} \:\:{also}\:{find}\:{the}\:{radius}\:{of}\:{this}\:{serie}.…

Question Number 49952 by maxmathsup by imad last updated on 12/Dec/18 $$1)simplify{A}_n=\frac{1}{{(2+i\sqrt{3})}^n}+\frac{1}{{(2-i\sqrt{3})}^n}$$$$2)smplify{B}_n=\frac{1}{{(2+\sqrt{3})}^n}+\frac{1}{{(2-\sqrt{3})}^n}$$$$nintegrnatural.$$ Commented…

Question Number 180901 by alcohol last updated on 19/Nov/22 $${\int }_1^n\frac{\lfloor x\rfloor }{x^2}dx=$$ Answered by srikanth2684 last updated on 19/Nov/22 $$\int_{\mathrm{1}} ^{\:\mathrm{2}} \frac{\lfloor{x}\rfloor}{{x}^{\mathrm{2}}…

Question Number 49809 by Abdo msup. last updated on 10/Dec/18 $$solvethesystem\{\begin{array}{l}\frac{4\sqrt{1+x^2}}{x}=\frac{5\sqrt{1+y^2}}{y}=\frac{6\sqrt{1+z^2}}{z}\\ x+y+z=xyz.\end{array}$$$$\begin{array}{c}\\ \end{array}\}$$ Commented by MJS last updated on 12/Dec/18…

Question Number 115261 by bobhans last updated on 24/Sep/20 $$Equationofcircletouchingtheline$$$$\mid x-2\mid +\mid y-3\mid =4willbe$$ Answered by john santu last updated on 24/Sep/20 $$centreofcircleisapoint(2,3)$$$${with}\:{radius}\:=\:\frac{\mid\mathrm{2}+\mathrm{3}−\mathrm{9}\mid}{\:\sqrt{\mathrm{2}}}\:=\mathrm{2}\sqrt{\mathrm{2}}…