1/a+1/b(1+a)+1/c(1+1/a)(1+1/b)+1/d(1+1/a)(1+1/b)(1+1/c)-(1+1/a)(1+1/b)(1+1/c)（1+1/d)

(a-1+1/b)(b-1+1/c)
= ab - a + a/c - b + 1 - 1/c + 1 - 1/b + 1/bc
= a/c - b + 2 - 1/b (cause 1/bc is a and 1/c is ab)
= a/c -(1-b)^2/b
That last term is positive, unless b=1 when it is z