What is the sum from k=1 to infinity of sin(1/k) ?

The sum from k=1 to infinity of sin(1/k) is diverges

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sum from k=1 to infinity of sin(1/k)

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

diverges

Solution steps

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

Apply Series Limit Comparison Test:

diverges

= diverges

n = 1 \sum \infty \frac{1}{( 3 n + 1 ) ^{2}}

n = 1 \sum \infty cos (\frac{11}{n})

n = 0 \sum \infty 3^{n} \cdot 7^{- n}

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

n = 1 \sum \infty \frac{2}{3 n + 7}

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