What is the sum from n=0 to infinity of (10n)/(4n+1) ?

The sum from n=0 to infinity of (10n)/(4n+1) is diverges

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sum from n=0 to infinity of (10n)/(4n+1)

n = 0 \sum \infty \frac{10 n}{4 n + 1}

diverges

Solution steps

n = 0 \sum \infty \frac{10 n}{4 n + 1}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 10 \cdot n = 0 \sum \infty \frac{n}{4 n + 1}

Apply Series Divergence Test:

diverges

= 10 diverges

= diverges

n = 1 \sum \infty \frac{9}{5 n ^{3}}

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

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

n = 1 \sum \infty \frac{2}{n ^{0.45}}

n = 0 \sum \infty \frac{n}{10 n ^{6} + 1}

What is the sum from n=0 to infinity of (10n)/(4n+1) ?
The sum from n=0 to infinity of (10n)/(4n+1) is diverges