Find the positive value of m for which the coefficient of x2 in the expansion of (1 + x)m is 6.

To find: the positive value of m for which the coefficient of x2 in the expansion of (1 + x)m is 6.


Formula Used:


General term, Tr+1 of binomial expansionis given by,


Tr+1 nCr xn-r yr where


nCr


Now, finding the general term of the expression, (1 + x)m , we get


Tr+1mCr


Tr+1mCr


The coefficient of is mC2


mC2=6


=6





m=3,-2


Since m cannot be negative. Therefore,


m=3


Thus, positive value of m is 3 for which the coefficient of x2 in the expansion of (1 + x)m is 6


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