(adsbygoogle = window.adsbygoogle || []).push({}); A question on infinities.....

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

[tex]\int_0^{\infty}exp(-x^2)=\frac{sqrt\pi}{2}[/tex]

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

[tex]\frac{sqrt\pi}{2}=

\sum_0^{\infty}\frac{a_n{\infty}^{n+1}}{n¡(n+1)}[/tex]

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)

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# A question on infinities .

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