The coefficient of x53 in the expansion ∑m=0100 100Cm(x−3)100−m 2m is
100C47
100C53
−100C53
−100C100
The given sigma is the expansion of
[(x−3)+2]100=(x−1)100=(1−x)100
Therefore, x53 will occur in T54.
T54=100C53(−x)53
Therefore, the coefficient is −100C53.