What is the sum from n=2 to infinity of 4/(ln(n^2)) ?

The sum from n=2 to infinity of 4/(ln(n^2)) is diverges

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sum from n=2 to infinity of 4/(ln(n^2))

n = 2 \sum \infty \frac{4}{ln ( n ^{2} )}

diverges

Solution steps

n = 2 \sum \infty \frac{4}{ln ( n ^{2} )}

Apply the constant multiplication rule:

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

= 4 \cdot n = 2 \sum \infty \frac{1}{ln ( n ^{2} )}

Apply Series Integral Test:

diverges

= 4 diverges

= diverges

What is the sum from n=2 to infinity of 4/(ln(n^2)) ?
The sum from n=2 to infinity of 4/(ln(n^2)) is diverges