Prove that
$^{n} C_{r + 1} + 2^{n} C_{r} +^{n} C_{r - 1} =$

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Solution

Given,
$^{n} C_{r + 1} + 2^{n} C_{r} +^{n} C_{r - 1}$
Now,
$\begin{matrix} \Rightarrow^{n} C_{r + 1} +^{n} C_{r} +^{n + 1} C_{r} \Rightarrow^{n} C_{r + 1} +^{n} C_{r - 1} =^{n + 1} C_{r} \Rightarrow^{n + 1} C_{r + 1} +^{n + 1} C_{r} =^{n + 2} C_{r + 1} \end{matrix}$

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