# Dirichlet's convergence test

## Primary tabs

Type of Math Object:
Theorem
Major Section:
Reference

## Mathematics Subject Classification

### questions re: Dirichlet's convergence

Should the second line be the summation from i=0 to i=n-1 and the summation from i=0 to i=m-2?

Also, in the last line, $\vert\sum_{i=m}^n a_ib_i\vert<\epsilon$ < infinity, therefore $\sum a_nb_n$ converges?

Thanks.

### Re: questions re: Dirichlet's convergence

Agree with first comment; the sums are not correctly indexed.

Re the last line, it is correct, but you are using the Cauchy criterion: I recommend you quote it.