Comparison Test(adsbygoogle = window.adsbygoogle || []).push({});

Consider the two infinite series ##\sum a_n## and ##\sum b_n## with ##a_n,b_n \geq 0## and ##a_n \leq b_n## for all ##n##.

If ##\sum b_n## is convergent so is ##\sum a_n##.

If ##\sum a_n## is divergent so is ##\sum b_n##.

Limit Comparison Test

Consider the two infinite series ##\sum a_n## and ##\sum b_n## with ##a_n \geq 0## and ##b_n > 0## for all ##n##. Define:

$$c = \lim_{n \rightarrow \infty} \frac{a_n}{b_n}$$

If ##c## is positive and finite then either both series converge or both series diverge.

Does it matter if the two series we're comparing have different starting points? I don't think it matters because we can always strip out a finite number of terms from one of the series until both series have the same starting point.

http://tutorial.math.lamar.edu/Classes/CalcII/SeriesCompTest.aspx

But according to this link, "in order to apply this test we need both series to start at the same place."

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Comparison tests for series

Loading...

Similar Threads - Comparison tests series | Date |
---|---|

I How does the limit comparison test for integrability go? | Apr 12, 2016 |

Bounding Argument for Comparison Test | Jun 3, 2015 |

Limit Comparison Test | Jan 9, 2015 |

Limit comparison test intuition | Aug 27, 2013 |

Calculus II i don't understand the proof for the limit comparison test | Jul 10, 2013 |

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