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#### issacnewton

##### Member

- Jan 30, 2012

- 61

Let \( a>0\) and \( z_1 > 0\) . define \( z_{n+1}=\sqrt{a+z_n} \) for all \( n\in \mathbb{N} \). Show that \( (z_n) \) converges and find the limit.

I am supposed to use monotone convergence theorem. For that I need to prove that the sequence is bounded and monotone. I can prove that its bounded below by \( 0 \), but I am having trouble about the upper bound. Also sequence can be increasing or decreasing, depending upon the values

of \( a\) and \( z_1 \) . Any hints ?