binom{n}{r+1} + 2binom{n}{r} + binom{n}{r-1} | vedclass

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(B) We use the Pascal's identity: $\binom{n}{k} + \binom{n}{k-1} = \binom{n+1}{k}$.Given expression: $\binom{n}{r+1} + 2\binom{n}{r} + \binom{n}{r-1}$

Vedclass · Accepted Answer

$\binom{n+2}{r+1}$

Vedclass · Answer

(B) We use the Pascal's identity: $\binom{n}{k} + \binom{n}{k-1} = \binom{n+1}{k}$.Given expression: $\binom{n}{r+1} + 2\binom{n}{r} + \binom{n}{r-1}$.This can be rewritten as: $\left[ \binom{n}{r+1} + \binom{n}{r} \right] + \left[ \binom{n}{r} + \binom{n}{r-1} \right]$.Applying the identity:$= \binom{n+1}{r+1} + \binom{n+1}{r}$.Applying the identity again:$= \binom{n+2}{r+1}$.

$\binom{n}{r+1} + 2\binom{n}{r} + \binom{n}{r-1} = \dots$

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