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

The sum from n=1 to infinity of n/(cos(n)) is converges (absolutely)

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

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

converges (absolutely)

Solution steps

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

The series has positive and negative elements, check for conditional/absolute convergence

Check convergence of

n = 1 \sum \infty \frac{n}{cos ( n )} :

converges

= converges (absolutely)

n = 1 \sum \infty \frac{1}{n ^{2} - 4 n + 5}

n = 1 \sum \infty \frac{5}{e ^{n} - 1}

n = 44 \sum \infty \frac{5}{n ^{2} + 2 n}

n = 1 \sum \infty 9 (\frac{4}{5})^{n}

n = 0 \sum \infty 2 (\frac{1}{4})^{n}

What is the sum from n=1 to infinity of n/(cos(n)) ?
The sum from n=1 to infinity of n/(cos(n)) is converges (absolutely)