Give an example of infinite series where Sigma ak and sigma bk diverge, but sigma (ak - bk) converges.

Answer 1

The simplest way to solve this problem would be to start with a sequence that we know diverges, like the harmonic series: 1⁄1 + 1/2 + 1/3 + …

Try making a_k=1 + 1/2 + 1/3 + 1/4 + … and make b_k= 1/2 + 1/3 + 1/4 + ….

Then when you subtract the two series, the difference is exactly 1