Question

115+114*15+113*14+112*13+111*12

Answer 1

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