The largest value of n for which the series $$\sum_{k=1}^\infty\frac{1}{k^n}$$ diverges is n = 1, as established by the integral test. This series is known as the harmonic series, which is a classic example of a divergent series. For values of n greater than 1, the series converges. Understanding this concept is crucial for analyzing the behavior of p-series in mathematical analysis.
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eddybob123 said: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.