4 "cell_type": "markdown",
7 "$f(n) = 1 + \\frac{1}{1 + f(n-1)}$\n",
9 "$f(1) = \\frac{3}{2}$\n",
11 "$f(2) = 1 + \\frac{1}{1 + f(1)} = 1 + \\frac{1}{1 + \\frac{3}{2}} = 1 + \\frac{1}{\\frac{5}{2}} = 1 + \\frac{2}{5} = \\frac{7}{5}$\n",
13 "$f(3) = 1 + \\frac{1}{1 + f(2)} = 1 + \\frac{1}{1 + \\frac{7}{5}} = 1 + \\frac{1}{\\frac{12}{5}} = 1 + \\frac{5}{12} = \\frac{17}{12}$\n",
15 "$f(n) = 1 + \\frac{1}{1 + \\frac{n}{d}} = 1 + \\frac{1}{\\frac{n+d}{d}} = 1 + \\frac{d}{n+d} = \\frac{n+2d}{n+d}$"
20 "execution_count": 11,
29 "execution_count": 11,
31 "output_type": "execute_result"
37 "(1..1000).each do\n",
38 " # puts \"#{n}, #{d}, #{n.to_s.length > d.to_s.length}\"\n",
39 " count += 1 if n.to_s.length > d.to_s.length\n",
40 " n, d = n + 2 * d, n + d\n",
47 "execution_count": null,
57 "display_name": "Ruby 2.4.0",
62 "file_extension": ".rb",
63 "mimetype": "application/x-ruby",