ChallengeMedium ShareChallenge · Medium problemEvaluate the alternating sum of the even-index binomial coefficients(1000)−(1002)+(1004)−⋯+(100100).\binom{100}{0}-\binom{100}{2}+\binom{100}{4}-\cdots+\binom{100}{100}.(0100)−(2100)+(4100)−⋯+(100100).A−450-4^{50}−450B−250-2^{50}−250C2502^{50}250D−251-2^{51}−251Check Show answer Walk through it step by step Practice more like this