Prove that
`((n),(r))+2((n),(r-1))+((n),(r-2))=((n+2),(r))`

Explanation

To prove that

\[ \binom{n}{r} + 2\binom{n}{r-1} + \binom{n}{r-2} = \binom{n+2}{r} \]

we will use the properties of binomial coefficients.

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