R - n C r - C t-1 When n -1000 and r -500

^n C _r/^n C _r 1 = n r + 1/r ⇒ r ^n C _r/^n C _r 1 = n r + 1 Put n = 1000 and r = 500, ⇒ n r + 1 = 1000 500 + 1 = 501 ...

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Greatest Binomial Coefficients

r × n C r / C...

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r × $\frac{^{n} C_{r}}{^{n} C_{r - 1}}$ When n = 1000 and r = 500

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r × $\frac{^{n} C_{r}}{^{n} C_{r - 1}}$ When n = 1000 and r = 500

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

1 \leq r \leq n

$^{n} C_{r} \div^{n} C_{r - 1}$ =

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

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

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

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