Attack the series

Calculus Level 3

∑ n = 2 ∞ 1 ln ⁡ ( ln ⁡ ( n ) ) \sum_{n=2}^{\infty} \dfrac{1}{\ln(\ln(n))}

Determine whether the series above is convergent or divergent.

Convergent Divergent

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Kushal Bose by Kushal Bose , 28, India

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1 solution

1 l n ( l n ( n ) ) ≥ 1 n \frac{1}{ln(ln(n))} \geq \frac{1}{n}

As sum of HP is diverging, the required sum is also diverging.(By direct comparison test)

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