2
$\begingroup$

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 $\lim u_n$.

  • 1
    This 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

1 Answers 1