Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

I am struggling to prove the following identity

$$ 1 + y + \frac{1}{2!}y^2 + \frac{1}{3!}y^3 + \dots = lim_{N \to \infty} \sum_{r=0}^{N} \frac {N!}{r! (N-r)!} \frac{y}{N}^{r} = lim_{N \to \infty} (1 + \frac{y}{N})^N $$

any hint would the most appreciated. I understand the left-most term is the Taylor series for the exponential function, and the right-most term is also used as a definition of such function, yet I would like to know how the two are explicitly shown to be equivalent.

Thanks as usual

**Physics Forums | Science Articles, Homework Help, Discussion**

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

# Exponential Identities

Loading...

Similar Threads for Exponential Identities |
---|

A How to Convert a Complex Logarithm to a Complex Exponential |

I Decomposing a Certain Exponential Integral |

A Angular Moment Operator Vector Identity Question |

**Physics Forums | Science Articles, Homework Help, Discussion**