First slide

Binomial theorem for positive integral Index

Question

The value of $^{15} C_{0}^{2} -^{15} C_{1}^{2} +^{15} C_{2}^{2} - ... -^{15} C_{15}^{2}$ is

Moderate

A

15
B

$- 15$
C

0
D

51

Solution

As we know that $C_{0}^{2} -^{n} C_{1}^{2} +^{n} C_{2}^{2} -^{n} C_{2}^{2} + ... {(- 1)}^{n}^{n} C_{n}^{2} = 0$ (if n is odd) and in the question n=15(odd).
Hence sum of given series is 0.

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