Calc 2, Lec 23B: Prove Series ∑1/(n*ln(n)) Diverges with Integral Test

The infinite series ∑1/(n*ln(n)) (sum of 1/(n*ln(n))) diverges (n goes from 2 to infinity). This is not obvious since the terms 1/(n*ln(n)) go to zero faster than 1/n does as n goes to infinity. To prove ∑1/(n*ln(n)) diverges, we use the integral test. To do the resulting improper integral, we need to use substitution. We also need the fact that ln(ln(x)) goes to infinity (very, very slowly) as x goes to infinity.

#Calculus2 #IntegralTest #InfiniteSeries

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