# A question on infinities .

1. Mar 1, 2005

### eljose

A question on infinities.....

we all know that the function $$e^{-x^2}$$ can be expanded into a taylor series my question arises when we try to perform the integral:

$$\int_0^{\infty}exp(-x^2)=\frac{sqrt\pi}{2}$$

then if we expand exp(-x^2) in terms of its Taylor series and perform the integration we would find that:

$$\frac{sqrt\pi}{2}= \sum_0^{\infty}\frac{a_n{\infty}^{n+1}}{n¡(n+1)}$$

the question is if a sum of infinities can give a finite number such as happens in the last sum... where the a_n are the taylor coefficients of the series expansion for exp(-x^2)

Last edited: Mar 1, 2005
2. Mar 1, 2005

### matt grime

The sum makes no sense: you're not even adding up real numbers. At least take limits first, and then ask if it is permissible to interchange limits and summation signs. (answer, not always - this is basic analysis, not number theory.)

3. Mar 1, 2005

### mathman

To evaluate the integral, the simplest approach that works is first square it, then change the variables in the double integral to polar coordinates. You will then very easily get pi/4 for the squared integral.