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

The sum from n=0 to infinity of arctan(1/n) is diverges

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sum from n=0 to infinity of arctan(1/n)

n = 0 \sum \infty arctan (\frac{1}{n})

diverges

Solution steps

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

Apply Series Integral Test:

diverges

= diverges

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

n = 1 \sum \infty 3 (0.6)^{n - 1}

n = 1 \sum \infty \frac{2 ^{n}}{7 ^{n}}

n = 1 \sum \infty \frac{2}{6 ^{n}}

n = 1 \sum \infty n^{3} + 1

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