1. ## Series

If the series an is divergent then the series ran is also divergent for any given non-zero real number r.

I know that the result is true by intuition yet I have a difficulty in giving a rigorous proof.

Any help would be great!

2. ## Re: Series

Originally Posted by Kristen111111111111111111

If the series an is divergent then the series ran is also divergent for any given non-zero real number r.

I know that the result is true by intuition yet I have a difficulty in giving a rigorous proof.

Any help would be great!

3. ## Re: Series

Originally Posted by Kristen111111111111111111
For any finite "partial sum" $a_1+ a_2+ \cdot\cdot\cdot+ a_n$, the corresponding sum for $\sum ar_n$ is $ra_1+ ra_2+ \cdot\cdot\cdot+ ra_n= r(a_1+ a_2+ \cdot\cdot\cdot+ r_n)$.