First slide

Binomial theorem for positive integral Index

Question

$Sum of the last 12 coefficients in the binomial expansion of (1 + x)^{23} is$

Moderate

A

$2^{22}$
B

$2^{23}$
C

$2^{23} - {}^{23}C_{11}$
D

$2^{23} - 2^{11}$

Solution

$Sum of last 12 coefficients of (1 + x)^{23} is$
$S =^{23} C_{12} +^{23} C_{13} + \dots \dots +^{23} C_{23} \dots . . (1)$
$\begin{array}{l} {Using}^{n} C_{r} =^{n} C_{n - r} \\ we get S =^{23} C_{11} +^{23} C_{10} + \dots . . +^{23} C_{0} \dots \dots (2) \end{array}$
Adding (1) and (2),
$\begin{array}{l} we get 2 S =^{23} C_{0} +^{23} C_{1} + \dots . .^{23} C_{23} = 2^{23} \\ \Rightarrow S = 2^{22} \\ ∴ Sum of last 12 coefficients of (1 + x)^{23} is 2^{22} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App