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Let , m be the the smallest positive int...

Let , m be the the smallest positive interger such that the coefficient of `x^(2)` in the expansion of `(1+x)^(2)+(1+x)^(3)+....+(1+x)^(49)+(1+mx)^(50) " is " (3n+1)^(51)C_(3)` for some positive integer n . Then the value of n is ,

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