Question
My thought:
As far as the given equality is concerned, I can prove that the relation is true by calculating some general mathematics proving by L.H.S = R.H.S method(given in the picture below)
But I am curious if there is any specific formula of combinatorics which can fetch this equality.(without using this general LHS-RHS method)
Please help me into this.
If $x$ is the middle element in a subset of size $3$ drawn from $\{1,2,3,...,n+2\}$, how many choices are there for the remaining two elements? Now sum over $x$