Consider this wonderful ( think it is) identity $\begin{align*} &a+b(1+a) + c(1+a)(1+b) + d(1+a)(1+b)(1+c) +\cdots+l(1+a)(1+b)\cdots(1+k)\\ &\qquad= (1+a)(1+b)(1+c)\cdots(1+l)-1 \end{align*} $
I believe there must be some beautiful applications, for example deriving some other identities, of it. Can someone please explore these possibilities?