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 March 11th, 2015, 05:00 AM #1 Newbie   Joined: Mar 2015 From: bedfordshire Posts: 1 Thanks: 0 recurrence relations Hello, will someone please help me figure out how to if an+1=sqrt(2+an) Show that for all n ∈ N we have an+1 - an =(an- an-1)/(sqrt(2+an)+sqrt(2+an-1)) Last edited by skipjack; March 11th, 2015 at 05:53 AM.
 March 11th, 2015, 05:51 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 Divide $\large\text{a}_{n+1}^2 - a_n^2 = \text{a}_n - \text{a}_{n-1}$ by $\large\text{a}_{n+1} + a_n$.

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