1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Converging sequence

  1. Feb 27, 2007 #1
    1. The problem statement, all variables and given/known data

    Let t1=sqrt(2)

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

    What does it converge to?

    2. Relevant equations

    3. 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.
  2. jcsd
  3. Feb 27, 2007 #2
    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)
  4. Feb 28, 2007 #3


    User Avatar
    Science Advisor

    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!)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook