Continued fractions

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   For the continued fraction $[a_0; a_1, a_2]=[1; 3, 3]$, the convergent numerators satisfy $h_i=a_i h_{i-1}+h_{i-2}$ with $h_{-1}=1$ and $h_0=a_0$. Compute the numerator $h_2$ of the third convergent.

2. Warm-up

   For the continued fraction $[a_0; a_1, a_2]=[1; 2, 3]$, the convergent numerators satisfy $h_i=a_i h_{i-1}+h_{i-2}$ with $h_{-1}=1$ and $h_0=a_0$. Compute the numerator $h_2$ of the third convergent.

3. Warm-up

   For the continued fraction $[a_0; a_1, a_2]=[2; 3, 3]$, the convergent numerators satisfy $h_i=a_i h_{i-1}+h_{i-2}$ with $h_{-1}=1$ and $h_0=a_0$. Compute the numerator $h_2$ of the third convergent.

Problems shown under their original terms: Generated (template, solver-computed).