What is the sum from n=0 to infinity of n/(4n+1) ?

The sum from n=0 to infinity of n/(4n+1) is diverges

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sum from n=0 to infinity of n/(4n+1)

n = 0 \sum \infty \frac{n}{4 n + 1}

diverges

Solution steps

n = 0 \sum \infty \frac{n}{4 n + 1}

Apply Series Divergence Test:

diverges

= diverges

n = 1 \sum \infty sin (\frac{nπ}{2})

n = 0 \sum \infty (\frac{4}{5})^{2 n}

n = 1 \sum \infty 5 ln (\frac{n}{n + 1})

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

n = 0 \sum \infty \frac{n}{1 + n ^{4}}

What is the sum from n=0 to infinity of n/(4n+1) ?
The sum from n=0 to infinity of n/(4n+1) is diverges