Let ${u_n}$ be a real sequence defined by $$ u_1=2, ~ u_2=0, ~ u_{n+2 } =\frac{1}{2^{u_n}} + \frac{1}{2} $$ Prove that ${u_n}$ has finite limit and find $\lim u_n$.
$u_{n+2}=\frac{1}{2^{u_n}}+\frac{1}{2}$. find $\lim u_n$
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calculus
real-analysis
sequences-and-series
limits
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1This series is composed of 4 sub series, all of which are monotonic and bounded, try to show that, and show that all converge to the same limit. – 2012-11-26