What is the sum from n=1 to infinity of (5n)/(5n+1) ?

The sum from n=1 to infinity of (5n)/(5n+1) is diverges

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sum from n=1 to infinity of (5n)/(5n+1)

n = 1 \sum \infty \frac{5 n}{5 n + 1}

diverges

Solution steps

n = 1 \sum \infty \frac{5 n}{5 n + 1}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{n}{5 n + 1}

Apply Series Divergence Test:

diverges

= 5 diverges

= diverges

k = 1 \sum \infty \frac{5}{k ( k + 2 )}

n = 1 \sum \infty \frac{3}{e ^{n} - 1}

n = 2 \sum \infty 2 e^{- 4 n}

n = 1 \sum \infty \frac{i}{5 ^{n}}

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

What is the sum from n=1 to infinity of (5n)/(5n+1) ?
The sum from n=1 to infinity of (5n)/(5n+1) is diverges