Đáp án:
$\dfrac{1}{220500}$
Giải thích các bước giải:
$\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{1+2}}{1+2+3}}{1+2+3+4}}{1+2+3+4+5}}{1+2+3+4+5+6}}{\dfrac{1+2+3+4+5+6+7}{\dfrac{1+2+3+4+5+6}{\dfrac{1+2+3+4+5}{\dfrac{1+2+3+4}{\dfrac{1+2+3}{\dfrac{1+2}{1}}}}}}}\\=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{3}}{3+3}}{3+3+4}}{3+3+4+5}}{3+3+4+5+6}}{\dfrac{3+3+4+5+6+7}{\dfrac{3+3+4+5+6}{\dfrac{3+3+4+5}{\dfrac{3+3+4}{\dfrac{3+3}{\dfrac{3}{1}}}}}}}\\=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{3}}{6}}{6+4}}{6+4+5}}{6+4+5+6}}{\dfrac{6+4+5+6+7}{\dfrac{6+4+5+6}{\dfrac{6+4+5}{\dfrac{6+4}{\dfrac{6}{3}}}}}}\\=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{18}}{6+4}}{6+4+5}}{6+4+5+6}}{\dfrac{6+4+5+6+7}{\dfrac{6+4+5+6}{\dfrac{6+4+5}{\dfrac{6+4}{2}}}}}\\=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{1}{18}}{10}}{10+5}}{10+5+6}}{\dfrac{10+5+6+7}{\dfrac{10+5+6}{\dfrac{10+5}{\dfrac{10}{2}}}}}\\=\dfrac{\dfrac{\dfrac{\dfrac{1}{180}}{10+5}}{10+5+6}}{\dfrac{10+5+6+7}{\dfrac{10+5+6}{\dfrac{10+5}{5}}}}\\=\dfrac{\dfrac{\dfrac{\dfrac{1}{180}}{15}}{15+6}}{\dfrac{15+6+7}{\dfrac{15+6}{\dfrac{15}{5}}}}\\=\dfrac{\dfrac{\dfrac{1}{2700}}{21}}{\dfrac{21+6+7}{\dfrac{21+6}{3}}}\\=\dfrac{\dfrac{1}{56700}}{\dfrac{27+6}{\dfrac{27}3}}\\=\dfrac{\dfrac{1}{56700}}{\dfrac{35}{9}}\\=\dfrac{1}{220500}$
