This is an exercise from the lecture slides of the calculus course I'm taking. I can't figure this one out so I'm posting it here! 
I know the sequence converges by Cauchy criterion from the fact that the $|x_n - x_{n+1}| < \frac{1}{2^n}$ for all natural number $n$ implies the sequence is Cauchy.
The subsequence ${x_{2n+1}}$ is supposed to be easy to evaluate...