Let m be the smallest positive integer such that the coefficient of x2 – InterviewSolution

1.	Let m be the smallest positive integer such that the coefficient of x2 in the expansion of (1+x)2+(1+x)3+...+(1+x)49+(1+mx)50 is (3n+1)51C3 for some positive integer n. Then the value of n is
Answer» Let $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(1 + x)^{2} + (1 + x)^{3} + . . . + (1 + x)^{49} + (1 + m x)^{50}$ is $(3 n + 1)^{51} C_{3}$ for some positive integer $n$ . Then the value of $n$ is

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