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March 11th, 2015, 05:00 AM   #1
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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.
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March 11th, 2015, 05:51 AM   #2
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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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