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Let m be the smallest positive integer s...

Let m be the smallest positive integer 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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