# Infinite series

jaqueh

## Homework Statement

What does the series converge to?
[a1]=√12
[an+1]=√(12+an)

## Homework Equations

Let L = the limit it approaches

## The Attempt at a Solution

I don't know if i did this correctly but I made
L = √(12+√(12+√(12+...)))
then L2 = 12+√(12+√(12+...))
then L = 12 + 12∞-1...12
thus L = ∞√(12 + 12∞-1...12)

#### Attachments

• Screen shot 2011-12-06 at 10.38.40 PM.png
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## Answers and Replies

Science Advisor
Homework Helper
If it converges then a_n approaches L as n->infinity. So does a_(n+1). Put that into a_n=sqrt(12+a_(n+1)).

jaqueh
If it converges then a_n approaches L as n->infinity. So does a_(n+1). Put that into a_n=sqrt(12+a_(n+1)).

ok i get that an+1 converges now because it is in the an series, but what is the limit that it approaches?

Science Advisor
Homework Helper
ok i get that an+1 converges now because it is in the an series, but what is the limit that it approaches?

It approaches the same limit as a_n, call it L. Solve for L!