Hello!(adsbygoogle = window.adsbygoogle || []).push({});

Unfortunately, I have not spent as much time as I should have on limits, or sequences, or their properties. In trying to work on a number theory math proof I have come across the following:

I have an infinite sequence of numbers, all between 0 and 1 inclusive. I know that the limit of this sequence is 0.4. I know that at some point, call it x, where x is the nth term in the sequence, all the numbers in the sequence past x get very close to the limit (in fact as close as I would like). For example, I know already that for n = 1 million, all the numbers past x will be within 0.001 of 0.4.

However, what I need to know is information about the numbers BEFORE my currently known x. So what I would like to know is if there are tests that can find a less precise bound on a sequence that has a known limit.

For instance, (if it were true) is there a test that would tell me that for n = 50, all the numbers in the sequence past x will be within 0.4 of 0.4? More specifically, are there tests that will tell me the most IMPRECISE bound on the sequence? (Aside from the given bound of between 0 and 1, since it's possible none of the numbers will ever actually be 0 or 1)

(And then, I actually have an infinite series of such sequences, and none of them have quite the same properties, nor quite the same limits, although all the limits are known; so I assume it's possible I might need different tests depending on which particular sequence I was looking at.)

And for those that are curious, since limits are usually the important part, the numbers that actually contain the information I need are usually within the first 0.1% of the numbers that are before my currently known x's. (So for all the sequences I know an x such as the example I used at the start where n = 1 million; but all the important information for that particular sequence comes from the first 1000 numbers. (However, some of the sequences still have billions of important numbers, its simply that the known bound for the limit occurs at a VERY high n value.)

**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!

# Bounds on infinite sequences with a known limit

Loading...

Similar Threads - Bounds infinite sequences | Date |
---|---|

Insights Hilbert Spaces And Their Relatives - Part II - Comments | Mar 6, 2018 |

I Gluing lemma / infinite corollary | Sep 17, 2017 |

I For direct proof, how do you choose M for bounded sequence? | Feb 16, 2017 |

A Finding the bounds of a ratio | Aug 30, 2016 |

General Theorems on Bounding Manifolds? | Dec 12, 2014 |

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