What is the sum from n=3 to infinity of 2/(nln^2(n)) ?

The sum from n=3 to infinity of 2/(nln^2(n)) is converges

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sum from n=3 to infinity of 2/(nln^2(n))

n = 3 \sum \infty \frac{2}{n ln ^{2} ( n )}

converges

Solution steps

n = 3 \sum \infty \frac{2}{n ln ^{2} ( n )}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 2 \cdot n = 3 \sum \infty \frac{1}{n ln ^{2} ( n )}

Apply Series Integral Test:

converges

= 2 converges

= converges

What is the sum from n=3 to infinity of 2/(nln^2(n)) ?
The sum from n=3 to infinity of 2/(nln^2(n)) is converges