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Q.

The value of the sum  1000C50+999C49+998C48+…+950C0 is

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a

1001C50

b

1002C951

c

1001C950

d

1002C50

answer is A.

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Detailed Solution

1000C50+999C49+998C48+…+950C0= coefficient of x950 in (1+x)950+(1+x)951+…+(1+x)1000= coefficient of x950 in (1+x)950(1+x)51−1(1+x)−1= coefficient of x950 in (1+x)1001−(1+x)950x= coefficient of x951 in (1+x)1001=1001C951=1001C50
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