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[" 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)^(5i)C_(3)" for some positive integern."],[" Then the value of "n" is "]

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