What is the coefficient of `x^(100)` in the expansion of `(1+x+x^2+x^3+.....+x^100)^3`

Explanation

`(1+x+x^2+x^3+...+x^100)^3`

Coefficient of `x^n` in an expression `(x_1+x_2+...+x_m)` can be given as `C(n+m-1,n)`.

Here, `n =100, m = 3`.

`:.` Coefficient of 100th term in given expression ` = C(100+3-1,100) = C(102,100) = C(102,2)`.

so, option `C` will be the correct option.