Category: Arithmetic

Question Number 138842 by peter frank last updated on 18/Apr/21 $$Findthesumtoinfinity$$$$1+\frac{3x}{1!}+\frac{5x^2}{2!}+\frac{7x^3}{3!}+..$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 7743 by Tawakalitu. last updated on 13/Sep/16 $$Allthetermsofthearithmeticprogession$$$$u_1,u_2,u_3,\dots u_{n}arepositive.useinductionto$$$$provethatforn⩾2$$$$\frac{\mathrm{1}}{{u}_{\mathrm{1}} {u}_{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{u}_{\mathrm{2}} {u}_{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{u}_{\mathrm{3}} {u}_{\mathrm{4}}…

Question Number 7723 by FilupSmith last updated on 12/Sep/16 $$p_n=n\mathrm{th}\mathrm{prime}(p_1=2,p_2=3,p_3=5,\dots )$$$$\mathrm{Do}\mathrm{the}\mathrm{following}\mathrm{sums}\mathrm{converge}?\mathrm{Prove}/\mathrm{disprove}.$$$$\left(1\right)S=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{n}{p_n}$$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{{p}_{{n}}…

Question Number 138698 by mathlove last updated on 16/Apr/21 Answered by nimnim last updated on 16/Apr/21 $$\frac{a}{b}=1.454545\dots ..=\frac{145-1}{99}=\frac{144}{99}=\frac{16}{11}$$$$\Rightarrow a=16,b=11$$$$\therefore a+b=16+11=27$$ Commented by…

Question Number 7590 by FilupSmith last updated on 05/Sep/16 $$S=\underset{n=2}{\sum ^k}\frac{2(n+1)}{n(n-1)}$$$$S=?$$ Commented by Yozzia last updated on 05/Sep/16 $$\frac{\mathrm{2}\left({n}+\mathrm{1}\right)}{{n}\left({n}−\mathrm{1}\right)}\equiv\frac{{a}}{{n}}+\frac{{b}}{{n}−\mathrm{1}} \…