Exponential of Zero/Proof 3

Theorem

$\exp 0 = 1$

Proof

This proof assumes the power series definition of $\exp$.

That is, let:

$\ds \exp x = \sum_{k \mathop = 0}^\infty \frac {x^k} {k!}$

Then:

\(\ds \exp 0\)

\(=\)

\(\ds \sum_{k \mathop = 0}^\infty \frac {0^k} {k!}\)

\(\ds \)

\(=\)

\(\ds 1\)

Definition of Power of Zero

$\blacksquare$