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

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detailed solution

Correct option is C

As we know that C02− C12+C22− C32+⋯+(−1)nCn2=0(if n is odd) and in the question n = 15 (odd). Hence, sum of given series is 0.

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The value of 15C0 2- 15C1 2+ 15C2 2−⋯− 15C15 2 is

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