Suppose I have a sequence(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a_0 = 1[/tex]

[tex]a_n = \sum_{k=1}^n f(k)\cdot a_{n-k}[/tex]

where f(n) is a known function (in binomial coefficients, powers, and the like).

In general, how would I go about proving that [itex]a_n\sim g(n)[/itex]? I'm working on more closely estimating the function by calculating its value for large n, along with first and second differences. (Suggestions on better methods are welcome, though I think I'm nearly there -- the second differences look suspiciously hyperbolic.)

Any help would be appreciated.

**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!

# Proving asymptotics to sequences

Loading...

Similar Threads - Proving asymptotics sequences | Date |
---|---|

I Proving that an operator is unbounded | Feb 8, 2018 |

I Proving a set is linearly independant | Apr 14, 2017 |

I Proving a property when elements of a group commute | Mar 29, 2017 |

Asymptotic formula for the sum of log(p)/p | Jan 19, 2012 |

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