Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 88471 by M±th+et£s last updated on 10/Apr/20

Answered by mr W last updated on 10/Apr/20

$$a_{n+1}=2+\frac{5}{a_n}$$$$\underset{n\to \mathrm{\infty }}{\lim }{a}_{n+1}=\underset{n\to \mathrm{\infty }}{\lim }(2+\frac{5}{a_n})$$$$l=2+\frac{5}{l}$$$$l^2-2l-5=0$$$$\Rightarrow l=1+\sqrt{6}$$

Commented by M±th+et£s last updated on 10/Apr/20

$$\text{Double subscripts: use braces to clarify}$$

Commented by M±th+et£s last updated on 10/Apr/20

$$sorryimean\underset{n\to \mathrm{\infty }}{lim}{a}_n$$

Commented by M±th+et£s last updated on 11/Apr/20

$$andcanwefind{a}_n$$

Commented by mr W last updated on 11/Apr/20

$$ifconvergenceexists,i.e.$$$$\underset{n\to \mathrm{\infty }}{\lim }{a}_n=l,thatmeanswhenn\to \mathrm{\infty },$$$$a_n\to l$$$$then{it}^{\prime }sclear,whenn\to \mathrm{\infty },\Rightarrow n+2\to \mathrm{\infty }$$$$\Rightarrow a_{n+2}\to l,therefore:$$$$\underset{n\to \mathrm{\infty }}{\lim }{a}_{n+2}=l$$$$\underset{n\to \mathrm{\infty }}{\lim }{a}_{n+2000000}=l$$$$\underset{n\to \mathrm{\infty }}{\lim }{a}_{n-100}=l$$

Commented by mr W last updated on 11/Apr/20

$$i^{\prime }mnotsurethatwecangettheexplicit$$$$formfor{a}_n.$$

Commented by M±th+et£s last updated on 11/Apr/20

$$thankyousir$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com