Question 25
Arrange all positive integers less than 30 in a line, calculate the reciprocal of the product of every three successive numbers, then add the reciprocals to obtain S, that is; $S=\frac1{1\times2\times4}+\frac1{2\times4\times5}+\cdots+\frac1{26\times28\times29}$ . What is the numerator of S reduced to the simplest fraction?