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The $k=0$ term equals $1$ because substituting $k=0$ into the general term yields $\frac{(-1)^0 x^0}{0!}$. The video uses the standard conventions that $(-1)^0 = 1$, $x^0 = 1$, and $0! = 1$.

Conditions: The index value is $k=0$.; The standard mathematical conventions $x^0=1$ and $0!=1$ are assumed.

The $k=0$ term equals $1$ because substituting $k=0$ into the general term yields $\frac{(-1)^0 x^0}{0!}$. The video uses the standard conventions that $(-1)^0 = 1$, $x^0 = 1$, and $0! = 1$.

Conditions: The index value is $k=0$.; The standard mathematical conventions $x^0=1$ and $0!=1$ are assumed.