Bài giải:

Ta có:

$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}=\frac{15}{16}$

$\begin{align}\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}=\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+...+\frac{1}{11\times 12} \\=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{12} \\=1-\frac{1}{12} \\=\frac{11}{12} \\\end{align}$

=>$\frac{15}{16}:x=\frac{11}{12}$

$\begin{align}x=\frac{15}{16}:\frac{11}{12} \\x=\frac{45}{44} \\\end{align}$

Đáp số: $\frac{45}{44}$