So $(x^2 - 1/x)^{100}$

Through the binomial formula $(x^2 - 1/x)^{100}$ is:

$$\sum\_{j = 0}^{100} C(100,j) (x^{2})^{j} (1/x)^{100-j}$$

$$\sum\_{j = 0}^{100} C(100,j) (x^{2})^{j} (-1)^{100-j}(x^{-1})^{100-j}$$

$$\sum\_{j = 0}^{100} C(100,j) (x)^{2j} (-1)^{100-j}(x)^{-100+j}$$

$$\sum\_{j = 0}^{100} C(100,j) (x)^{3j-100} (-1)^{100-j}$$

Let k = $3j-100$

Then j = $(k+100)/3$

And k should any value between 0 and 100 inclusive such that k is a whole number.

I'm not sure what's wrong in how I proceeded, I know the correct answer should be:

$(-1)^{(200-k)/3} C(100,(200-k)/3)$

But I'm not sure where I went wrong