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Question
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
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Solution
\[= \left( {}^n C_{r + 1} +^n C_r \right) + \left( {}^n C_r +^n C_{r - 1} \right) \left[ {}^n C_r +^n C_{r - 1} =^{n + 1} C_r \right]\]
\[ = {}^{n + 1} C_{r + 1} +^{n + 1} C_r \left[ {}^n C_r +^n C_{r - 1} =^{n + 1} C_r \right]\]
\[ =^{n + 2} C_{r + 1} \]
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