Some metrical results on the approximation by continued fractions

Let $x$ be a real irrational number and $p_n/q_n, n=1,2,\ldots$ its sequence of continued fraction convergents. Define $d_n=q_{n+1}|q_nx-p_n|.$ For almost all $x$ the distribution functions of the sequences $|d_n-d_{n+1}|$ and $d_n+d_{n+1}$ are determined.