Thread: 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??

Originally Posted by Some1Godlier

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

Definitely not!

Consider

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.

well let both divergent series, but the difference converges.

of course, just a particular case.