Question 13
Arrange all positive integers less than 30 and not divisible by 3 in an increasing order, and compute the sum of the reciprocals of product of every three consecutive numbers, that is $S=\frac1{1\times2\times4}+\frac1{2\times4\times5}+\cdots+\frac1{26\times28\times29}$. Now, if we reduce $S$ into its simplest form, then what would be the value of the numerator?