1. ## Cauchy Sequences

I am asked to show that the following is a Cauchy sequence from the definition of a Cauchy sequence.

(1 + 1/(2!) + ... + 1/(n!))

I'm not really sure how to deal with the factorial. Any help would be much appreciated.

2. Originally Posted by jkru
I am asked to show that the following is a Cauchy sequence from the definition of a Cauchy sequence.

(1 + 1/(2!) + ... + 1/(n!))

I'm not really sure how to deal with the factorial. Any help would be much appreciated.
Try proving this. If $|a_{n+1}-a_n| \leq b_n$ and $\sum_{n=1}^{\infty} b_n < \infty$ then $\{ a_n\}$ is Cauchy.