Converging sequence

  • Thread starter akoska
  • Start date
  • #1
22
0

Homework Statement



Let t1=sqrt(2)

Let t_(n+1)=sqrt(2+sqrt(t_n)) (it's a recursively defined series)

What does it converge to?


Homework Equations





The Attempt at a Solution



I calculated it out for some values andI get 1.8312 (approx), but I don't want to express it in decimals, and I want to know if there's a good way to do this.
 

Answers and Replies

  • #2
19
0
Let's suppose it converges, then t_(n+1) and t_n will have a infinitesimally small difference as n approaches infinity, and you can consider them the same number. (aka the limit of this sequence)
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
961
I would have phrased it differently, but basically said the same thing. Since {tn+1[/b]} is exactly the same sequence as {tn}, just indexed differently, taking the limit as n goes to infinity gives the same value, say T, on both sides. Solve that equation for T. (That's not a trivial equation but there is one obvious root!)
 

Related Threads on Converging sequence

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
6
Views
889
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
2
Views
938
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
Top