# Thread: Does the subtraction of 2 diverging Series mean the resulting Series is convergent?

1. ## Does the subtraction of 2 diverging Series mean the resulting Series is convergent?

An=Bn-Cn Bn and Cn are both diverging Does An converge??

2. Originally Posted by Some1Godlier
An=Bn-Cn Bn and Cn are both diverging Does An converge??
Definitely not!

Consider $B_n=n^2 \text{ and} C_n=5n^4$

Clearly the difference diverges as well. The difference can sometimes lead to a converging series but you need to use convergence tests to verify. An example of such a case is a telescoping series, where almost all the terms cancel out and the remaining terms sum to a finite value.

3. well let $a_n=b_n=n,$ both divergent series, but the difference converges.

of course, just a particular case.