Sequence Problem

Calculus Level 2

Let a recurrent sequence be defined as:

u0:=2un+1:=12un+12,nN\begin{aligned} u_0 & := 2 \\ u_{n+1} & := \dfrac 12 u_n + \dfrac 12, & n \in \mathbb N \end{aligned}

Find limnun\displaystyle \lim_{n \to \infty} u_n .

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