First slide

Binomial theorem for positive integral Index

Question

The greatest term in the expansion of ${(1 + x)}^{10}$ when $x = 2 / 3$ is

Moderate

A

$210 (3 / 2)^{6}$
B

$210 (2 / 3)^{4}$
C

$210 (3 / 2)^{4}$
D

none of these

Solution

$α = \frac{(10 + 1) (2 / 3)}{1 + 2 / 3} = \frac{22}{5} \Rightarrow [α] = 4$
Thus, the greatest term is 5th term and it is given by
$^{10} C_{4} {(\frac{2}{3})}^{4} = 210 {(\frac{2}{3})}^{4}$

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