Prove that converges if and only if converges for any
Assume that the latter series converges then this inequality holds for some real
And thus does also the first series converge. They only differ by a constant depending on .
Now assume that diverges to for some and that converges.
This inequality holds for some
But this inequality doesn't hold for any
My assumtition must be wrong.
Either does both diverge to or converge.
Is there something wrong? Something missing to complete the proof?