What is the sum from n=2 to infinity of ((-1)^n)/(sqrt(n)ln(n)) ?

The sum from n=2 to infinity of ((-1)^n)/(sqrt(n)ln(n)) is converges

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sum from n=2 to infinity of ((-1)^n)/(sqrt(n)ln(n))

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

converges

Solution steps

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

Apply Alternating Series Test:

converges

= converges

\int 4 + y^{2} d y

\int \frac{14}{( x - 1 ) ^{2} ( x - 2 ) ^{2}} d x

f (x) = arcsin (4 x)

x \to \infty lim (arctan (x^{2} - x^{5}))

y = e^{x} ln (x), (1, 0)

What is the sum from n=2 to infinity of ((-1)^n)/(sqrt(n)ln(n)) ?
The sum from n=2 to infinity of ((-1)^n)/(sqrt(n)ln(n)) is converges