binom{n}{n-r} + binom{n}{r+1},whenever 0 le r | vedclass

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(D) We know that $\binom{n}{k} = \binom{n}{n-k}$.Therefore,$\binom{n}{n-r} = \binom{n}{r}$.Substituting this into the expression,we get:$\binom{n}{n-r

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$\binom{n+1}{r+1}$

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(D) We know that $\binom{n}{k} = \binom{n}{n-k}$.Therefore,$\binom{n}{n-r} = \binom{n}{r}$.Substituting this into the expression,we get:$\binom{n}{n-r} + \binom{n}{r+1} = \binom{n}{r} + \binom{n}{r+1}$.Using the Pascal's identity formula $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1}$,we obtain:$\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1}$.

$\binom{n}{n-r} + \binom{n}{r+1}$,whenever $0 \le r \le n-1$,is equal to

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