Today, my professor said something like "The series 1 + -1 + 1 + -1 and so on is defined to be one half... but let's not go into that." and then didn't feel like explaining when people asked him why. I have no idea why that would be true...(adsbygoogle = window.adsbygoogle || []).push({});

It seems like a similar case might be

[tex]\int_{0}^{\infty}\sin x\,\textrm{d}x[/tex]

but that isn't defined to be one half or zero or anything at all.

So why oh why is this true?

[tex]\sum_{n=0}^{\infty}\left(-1\right)^{n}=\frac{1}{2}[/tex]

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Odd series behavior?

Loading...

Similar Threads - series behavior | Date |
---|---|

I Help with simplifying series of hyperbolic integrals | Nov 19, 2017 |

I Taylor series | Jul 21, 2017 |

I How to understand Taylor/Mclaurin series? | May 19, 2017 |

B Series expansion of velocities | Apr 1, 2017 |

Asymptotic behavior of a power series near its branch point | May 1, 2013 |

**Physics Forums - The Fusion of Science and Community**