is there any formula can calculate it directly?


As we known, the sum of all binomial coefficients of (1 + x)^n is 2^n. Now if we want to randomly calculate the partial sum (from first term to k-th term) of them, is there any formula can calculate it directly? first of all, the sum of former (n/2) terms is exactly (2^n)/2 when n is odd. Second, the sum of first and second terms is (1+n). And then...













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