I was assigned to compute the group homology of $\mathbb{Z}^k$ with $\mathbb Z$ as coefficient ring(with the trivial action): $H_*(\mathbb{Z}^k, \mathbb{Z})$.
I know that $H_*(\mathbb{Z}^k, \mathbb{Z}) = {\rm Tor} _* ^{\mathbb{Z}(\mathbb{Z}^k)}(\mathbb{Z}, \mathbb{Z}) $, but I don't know how to compute this Tor. I think, first of all, I need to take a projective resolution of $\mathbb{Z}$, but even I am stuck with it. Is there any easy way to compute this?
I have more problems which I have to do. If someone help me on this, then I will try to solve the others by myself. Thank you for your help!