Infinite series

  • Thread starter jaqueh
  • Start date
  • #1
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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)
 

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Answers and Replies

  • #2
Dick
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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)).
 
  • #3
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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?
 
  • #4
Dick
Science Advisor
Homework Helper
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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!
 

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