First slide

Binomial theorem for positive integral Index

Question

If $α$ and $β$ are the coefficients of $x^{r}$ and $x^{n - r}$ respec-tively in the expansion of $(1 + x)^{n}$ , then

Moderate

A

$α = β$
B

$α + β = n$
C

$α = k β$ for some constant $k$
D

$α + β = 2^{n}$

Solution

$α =^{n} C_{r}$ and $β =^{n} C_{n - r}$
$∴ α = β$

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