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

The sum from n=1 to infinity of 1/(cos^2(n)) is diverges

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sum from n=1 to infinity of 1/(cos^2(n))

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

diverges

Solution steps

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

Apply Series Comparison Test:

diverges

= diverges

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

n = 0 \sum \infty \frac{2}{n + 2}

n = 0 \sum \infty \frac{1}{16 n ^{2} - 4}

n = 1 \sum \infty (0.7)^{n - 1}

n = 0 \sum \infty \frac{1}{n + 2} - \frac{1}{n}

What is the sum from n=1 to infinity of 1/(cos^2(n)) ?
The sum from n=1 to infinity of 1/(cos^2(n)) is diverges