Combo Algebra

Probability Level 3

Compute (1001)+2(1002)++100(100100). \dbinom{100}{1} + 2\dbinom{100}{2} +\ldots + 100\dbinom{100}{100}. If your answer is k2n k \cdot 2^n , where nn and kk are positive integers and kk is odd, find n+k n+k .

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