Let \(G_{n} \sim \mathrm{N}\left(0, t_{n}ight), n \geqslant 1\), be sequence of Gaussian random variables. Show that \(G_{n} \xrightarrow{\mathrm{d}} G\) if, and only if, the sequence \(\left(t_{n}ight)_{n \geqslant 1}\) is convergent.