Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 19 / b / i

A constant sequence must satisfy the fixed point equation $y_{\ast }=\sqrt{2+y_{\ast }}$. The square root forces $y_{\ast }\ge 0$. Squaring gives $(y_{\ast }-2)(y_{\ast }+1)=0$, so the negative algebraic root is inadmissible. HenceStarting at $y_0=2$ produces the constant sequence $2,2,\dots$.