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