First slide

Binomial theorem for positive integral Index

Question

If $C_{r}$ stands for ${}^{n}C_{r},$ then the sum of first ( n + 1 ) terms of the $(n + 1)$ terms of the series $a C_{0} - (a + d) C_{1} + (a + 2 d) C_{2} - (a + 3 d) C_{3} + \dots$ , is

Moderate

A

$\frac{a}{2^{n}}$
B

$n a$
C

0
D

none of these

Solution

We have,
$a C_{0} - (a + d) C_{1} + (a + 2 d) C_{2} - (a + 3 d) C_{3} + \dots . . . . . . . . . . + (- 1)^{n} (a + n d) C_{n}$

$\begin{array}{l} = \sum_{r - 0}^{n} (a + r d) {(- 1)^{r}}^{n} C_{r} \\ = a \sum_{r = 0}^{n} {(- 1)^{r}}^{n} C_{r} - d n \sum_{r = 1}^{n - 1}^{n - 1} C_{r - 1} {(- 1)^{r}}^{1} \\ = a \times 0 - d n \times 0 = 0 \end{array}$

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