= Solution
For <independent and identically distributed random variables> $X_j\sim\mathcal N(0,\sigma^2)$, the <linear combination of independent normal random variables> $n^{-1/2}\sum_{j=1}^nX_j$ has <expected value> zero and <variance> $n^{-1}n\sigma^2=\sigma^2$. Thus
$$
\boxed{n^{-1/2}(X_1+\cdots+X_n)\sim\mathcal N(0,\sigma^2)\quad(n\geq1).}
$$
This is exactly the requested $2$-stability. The paper's definition is a <strictly stable distribution>, since it allows no centering term.
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