Question 6
After simplification, the following value is a proper fraction in lowest terms. Find its denominator minus its numerator.
$$1-\frac2{1(1+2)}-\frac3{(1+2)(1+2+3)}$$
$$-\frac4{(1+2+3)(1+2+3+4)}-\cdots-\frac{100}{(1+\cdots+99)(1+\cdots+100)}.$$
$$1-\frac2{1(1+2)}-\frac3{(1+2)(1+2+3)}$$
$$-\frac4{(1+2+3)(1+2+3+4)}-\cdots-\frac{100}{(1+\cdots+99)(1+\cdots+100)}.$$