The correct option is A 1001C50
Clearly, the given series is a geometric progression in which
a=(1+x)1000,r=x(1+x)999(1+x)1000=x(1+x) and n=1001.
∴ Given sum =a(1−rn)(1−r)
=(1+x)1000×{1−(x1+x)1001}(1−x1+x)
=(1+x)1001−x1001
∴ Coefficient of x50 in the above expansion = 1001C50