= Solution
A one-dimensional commutative <formal group law> over a ring $R$ is a series $F(X,Y)\in R[[X,Y]]$ satisfying
$$
F(X,0)=X,
\qquad F(X,Y)=F(Y,X),
\qquad F(F(X,Y),Z)=F(X,F(Y,Z)).
$$
The identity axiom gives $F(X,Y)=X+Y+$ terms of total degree at least two. Seek
$$
i(X)=-X+a_2X^2+a_3X^3+\cdots.
$$
After $a_2,\ldots,a_{n-1}$ have been chosen, the coefficient of $X^n$ in $F(X,i(X))$ is $a_n$ plus a known expression in the earlier coefficients. There is therefore a unique choice of $a_n$ making it zero. Recursion constructs the <formal inverse> $i(X)$ with $F(X,i(X))=0$ and $i(X)\equiv-X\pmod{X^2}$.
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