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)^4 +........+ (1+x)^49 + (1 + mx)^50` is `(3n + 1) .^51C_3` for some positive integer n. Then the value of n is

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