TITLE: what are the uses of this identity
QUESTION [5 upvotes]: 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?

REPLY [9 votes]: There is a whole article devoted to applications of this identity: Bhatnagar, In Praise of an Elementary Identity of Euler.