1\15+1\14*15+1\13*14+1\12*13+1\11*12

Решите задачу:

$\frac{1}{15}+\frac{1}{14*15}+\frac{1}{13*14}+\frac{1}{12*13}+\frac{1}{11*12}=\\\frac{1}{15}+\frac{1}{14}*\frac{1}{15}+\frac{1}{13}*\frac{1}{14}+\frac{1}{12}*\frac{1}{13}+\frac{1}{11}*\frac{1}{12}=\\\frac{1}{15}(1+\frac{1}{14})+\frac{1}{13}(\frac{1}{14}+\frac{1}{12})+\frac{1}{132}=\\\frac{1}{15}*\frac{15}{14}+\frac{1}{13}*\frac{13}{84}+\frac{1}{132}=\\\frac{1}{14}+\frac{1}{84}+\frac{1}{132}=\\\frac{6+1}{84}+\frac{1}{132}=\\\frac{1}{12}+\frac{1}{132}=\\\frac{11+1}{132}=\\\frac{1}{11}$