What is the formula of n^Cr

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Solution

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ⁿC_r = n! / (n-r)! x r!
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^{n} C_{r} + {4.}^{n} C_{r - 1} + {6.}^{n} C_{r - 2} + {4.}^{n} C_{r - 3} +^{n} C_{r - 4} =

^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r}

^{n} C_{r - 1} = 36,^{n} C_{r} = 84

^{n} C_{r + 1} = 126

^{n} C_{8}

\sum_{r = 1}^{n} r^{2}

\frac{^{n} C_{r}}{^{n} C_{r - 1}}

\frac{^{n} C_{r}}{^{n} C_{r + 1}} = \frac{1}{2}

\frac{^{n} C_{r + 1}}{^{n} C_{r + 2}} = \frac{2}{3}

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