First slide

Binomial theorem for positive integral Index

Question

$When x = \frac{5}{2}, numerically greatest term in the expansion of (3 + 2 x)^{15} is$

Easy

A

$6^{t h}$
B

$8^{t h}$
C

$10^{t h}$
D

$12^{t h}$

Solution

$Use the formula \frac{(n + 1) | x |}{1 + | x |} in (1 + x)^{n} {(3 + 2 x)}^{15} = 3^{15} {(1 + \frac{2 x}{3})}^{15} \frac{(n + 1) | x |}{1 + | x |} = \frac{(15 + 1) | \frac{2 x}{3} |}{1 + | \frac{2 x}{3} |} = \frac{16 (\frac{5}{3})}{1 + \frac{5}{3}} = \frac{80}{8} = 10 10 t h, 11 t h t e r m s a r e n u m e r i c a l l y g r e a t e s t t e r m s .$

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