What is the sum from n=1 to infinity of n/(csc(1/n)) ?

The sum from n=1 to infinity of n/(csc(1/n)) is diverges

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sum from n=1 to infinity of n/(csc(1/n))

n = 1 \sum \infty \frac{n}{csc ( \frac{1}{n} )}

diverges

Solution steps

n = 1 \sum \infty \frac{n}{csc ( \frac{1}{n} )}

Use the basic trigonometric identity:

\frac{1}{csc ( x )} = sin (x)

= n = 1 \sum \infty n sin (\frac{1}{n})

Apply Series Divergence Test:

diverges

= diverges

\int \frac{( arctan ( x ) ) ^{4}}{1 + x ^{2}} d x

\frac{\partial}{\partial x} (y ln (x^{3} + y^{4} + 2))

\frac{d}{d x} (e^{x z (x)})

f (x) = x^{2} + 169 x + 820, at x = 2

y = \frac{2 x}{7 - cot ( x )}

What is the sum from n=1 to infinity of n/(csc(1/n)) ?
The sum from n=1 to infinity of n/(csc(1/n)) is diverges