First slide

Binomial theorem for positive integral Index

Question

The value of ${(^{15} C_{0}^{})}^{2} - {(^{15} C_{1}^{})}^{2} + {(^{15} C_{2}^{})}^{2} - \dots - {(^{15} C_{15}^{})}^{2}$ is

Moderate

A

15
B

-15
C

0
D

51

Solution

As we know that ${C_{0}}^{2} -^{} C_{1}^{2} + C_{2}^{2} -^{} C_{3}^{2} + \dots + (- 1)^{n} C_{n}^{2} = 0$
(if n is odd) and in the question n = 15 (odd).
Hence, sum of given series is 0.

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