Bài giải:

$S=\frac{1}{10}+\frac{2}{55}+\frac{3}{220}+\frac{4}{640}+\frac{5}{1504}$

$S\times 3=\frac{3}{10}+\frac{6}{55}+\frac{9}{220}+\frac{12}{640}+\frac{15}{1504}$

$S\times 3=\frac{3}{2\times 5}+\frac{6}{5\times 11}+\frac{9}{11\times 20}+\frac{12}{20\times 32}+\frac{15}{32\times 47}$

$S\times 3=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{20}+\frac{1}{20}-\frac{1}{32}+\frac{1}{32}-\frac{1}{47}$

$S\times 3=\frac{1}{2}-\frac{1}{47}$

$S\times 3=\frac{45}{94}$

$S=\frac{15}{94}$