Saturday

April 18, 2015

April 18, 2015

Posted by **Hannah** on Tuesday, July 7, 2009 at 8:15am.

- Math -
**Reiny**, Tuesday, July 7, 2009 at 9:10amA(n) = √(3 + √(3 + √(3 + ...))..) to infinity

let x = √(3 + √(3 + √(3 + ...))..)

square both sides

x^2 = 3 + √(3 + √(3 + √(3 + ...))..)

or

x^2 = 3 + x

x^2 - x - 3 = 0

by the formula

x = (1+√13)/2

= appr. 2.302775638... which I got by repeatedly doing the following on my calculator about 20 times

1. √3

2. =

3. +3

4. =

5. √

goto 2.

**Answer this Question**

**Related Questions**

Math - A sequence {an} is given by a1=root(3), a n+1 = root(3+an). show that {an...

calculus - A sequence{an} is given by a1=sqrt(2), an+1=sqrt(2*an). a) by ...

Calculus - Determine whether the sequence with the given nth term is monotonic. ...

Math - (a) Find the number c such that the limit below exists. Limit as x goes ...

Math - limit of (x,y)--->(1,0) of ln(1+y^2/x^2+xy)) Find the limit, if it ...

calculus - (a) Find the number c such that the limit below exists. Limit as x ...

trig - find the limit of the sequence if it exists tn= 6/n

trig - find the limit of the sequence if it exists tn= 6/n

Calculus 3 - Find the limit, if it exists, or show that the limit does not ...

Calculus 3 - Find the limit, if it exists, or show that the limit does not exist...