Question

Difficult infinite series Question:
Suppose Sn represents the partial sum of a diverging infinite series, does the infinite sum 1/(Sk)^2 converge?

Answer 1

I tested it with the harmonic series and i'm pretty sure it diverges, but i can't prove this generally.

Answer 2

Depends on what s is equal to: I am reading this must behave like 1/2k^2 which converges, constant times a convergent p-series = 2

Answer 3

Sn is the partial sum of any diverging series. The p-series cannot be used as Sn is not a constant or bounded by a constant