Divergent Series: Finding the Largest Value of n

[eddybob123]

Hi all, is there any way to find what the largest value of n is such that $$\sum_{k=1}^\infty\frac{1}{k^n}$$ is divergent? I don't need an answer, I need an approach to the problem.

 

[Mark44]

Hi all, is there any way to find what the largest value of n is such that $$\sum_{k=1}^\infty\frac{1}{k^n}$$ is divergent? I don't need an answer, I need an approach to the problem.

Integral test.

It is well known that if n = 1, the series is the harmonic series, which diverges.