1

Question

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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)

enter image description here

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.

P db
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1 Answers1

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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 $x$

TomGrubb
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