Let $R$ be a noetherian complete local ring of positive residue characteristic $p>0$. A note I am reading states without proof that we have an isomorphism $$\varprojlim_{\nu}R[X]/\left((X+1)^{p^{\nu}}-1\right)\cong R[[X]]$$ This is allegedly a well-known isomorphism, and it holds because the residue characteristic is $p$.
I must admit that I am not really good at manipulating projective limits yet, and I'm a little at loss of idea in order to prove that such an isomorphism hold. Would anybody know what the strategy would be to prove this?