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$e^{A t}$ can be expanded as

1. $\sum_{k=0}^{\infty} \frac{\mathrm{A}^{k} t^{k}}{(k+1) !}$
2. $\sum_{k=0}^{\infty} \frac{\mathrm{A}^{k} t^{k}}{k !}$
3. $\sum_{k=0}^{\infty} \frac{\mathrm{A}^{k} t^{k+1}}{(k+1) !}$
4. $\sum_{k=0}^{\infty} \frac{\mathrm{A}^{k} t^{k+1}}{k !}$