# How come? Summation, identity?

1. Aug 1, 2015

### shanepitts

How does e22 ≈ 1-Δ22

When Δ<<δ ?

I'm sure it's a basic summation I'm unaware of.

2. Aug 1, 2015

### Number Nine

This comes from the Taylor expansion of the exponential function. Remember that
$$e^x = 1 + x + \frac{x^2}{2!} + \cdots = \sum_{i=0}^\infty \frac{x^i}{i!}$$
As $x$ gets very small, the lower order terms dominate (since the others go to zero), and so we can approximate the exponential function by taking the first few terms of the Taylor expansion.

Last edited: Aug 1, 2015