The coefficient of x50 in the binomial expansion of (1+x)1000+x(1+x)999+x2(1+x)998+….+x1000 is

Binomial coefficient (GP)E=(1+x)1000+x(1+x)999+x2(1+x)998+…+x1000(1+x)10001-x1+x10011-x/(1+x)=1+x1001-x1001∴ Coefficient of x50 in E=C50   1001=(1001)!(50)!(951)!