1.0 Exponential Series

Expansion of $e^x$ in terms of $x$ is given by, $${e^x} = 1 + \frac{x}{{1!}} + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + ... + \frac{{{x^r}}}{{r!}} + ...\infty $$ or $${e^x} = \sum\limits_{n = 0}^\infty {\frac{{{x^n}}}{{n!}}} $$

The above series is known as exponential series and $e^x$ is called exponential function.

The above series is used for solving a range of problems.