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

I want to show the convergence of the following series as N goes to infty.

[tex]\displaystyle{\sum_{k=0}^N}\frac{x^k}{k!}-\frac{n!x_n^k}{k!(n-k)!n^k}[/tex],

x_n is a sequence such that. lim(n->oo)x_n = x, but I´m interested in big N

I ´m not allowed to use the limit definition of exp(x)

What I want to do (but am not sure if it´s correct) is to separate the sum before taking the limit N->oo and after that take it, so that the first term converges to exp(x) an the convergence of the second term I can show with the ratio test

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

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!

# Convergence of the following series as N goes to infty

Loading...

Similar Threads - Convergence following series | Date |
---|---|

I Convergence of a recursively defined sequence | Mar 7, 2018 |

I What is this sequence that converges to ln(x) called? | Nov 21, 2017 |

A Gamma function convergence of an integral | Oct 11, 2017 |

B Not following an integral solution | Jun 16, 2017 |

I Divergence/Convergence for Telescoping series | Mar 25, 2017 |

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