Prove that .

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

Prove that (2nC0)2−(2nC1)2+(2nC2)2−⋯+(2nC2n)2=(−1)n⋅2nCn({}^{2n}C_0)^2 - ({}^{2n}C_1)^2 + ({}^{2n}C_2)^2 - \dots + ({}^{2n}C_{2n})^2 = (-1)^n \cdot {}^{2n}C_n .

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