What is the sum from n=0 to infinity of cos(1/(n^3)) ?

The sum from n=0 to infinity of cos(1/(n^3)) is diverges

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sum from n=0 to infinity of cos(1/(n^3))

n = 0 \sum \infty cos (\frac{1}{n ^{3}})

diverges

Solution steps

n = 1 \sum \infty cos (\frac{1}{n ^{3}})

Apply Series Divergence Test:

diverges

= diverges

n = 0 \sum \infty \frac{5}{2 n}

n = 0 \sum \infty n^{3} e^{- n^{2}}

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

n = 0 \sum \infty \frac{4}{5 ^{\frac{n}{3}}}

n = 0 \sum \infty \frac{1}{e}

What is the sum from n=0 to infinity of cos(1/(n^3)) ?
The sum from n=0 to infinity of cos(1/(n^3)) is diverges