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Evaluate the Following:N + 1cn - Mathematics

Evaluate the following:

n + 1Cn

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Solution

n + 1Cn =n + 1C1    [∵\[{}^n C_r = {}^n C_{n - r}\]]

\[\Rightarrow^{n + 1} C_n = {}^{n + 1} C_1 = \frac{n + 1}{1} \times {}^n C_0\]    [∵\[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]]
\[\Rightarrow\] n + 1Cn = n+1    [∵ \[{}^n C_0 = 1\]]
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.1 | Q 1.4 | Page 8
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