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Write the Expression Ncr +1 + Ncr − 1 + 2 × Ncr in the Simplest Form. - Mathematics

Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.

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Solution

\[{}^n C_{r + 1} + {}^n C_{r - 1} + 2 .^n C_r\]
\[= \left( {}^n C_{r + 1} +^n C_r \right) + \left( {}^n C_r +^n C_{r - 1} \right) \left[ {}^n C_r +^n C_{r - 1} =^{n + 1} C_r \right]\]

\[ = {}^{n + 1} C_{r + 1} +^{n + 1} C_r \left[ {}^n C_r +^n C_{r - 1} =^{n + 1} C_r \right]\]
\[ =^{n + 2} C_{r + 1} \]

Concept: Factorial N (N!) Permutations and Combinations
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 4 | Page 24
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