What is the sum from n=0 to infinity of (5n)/(10+n) ?

The sum from n=0 to infinity of (5n)/(10+n) is diverges

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sum from n=0 to infinity of (5n)/(10+n)

n = 0 \sum \infty \frac{5 n}{10 + n}

diverges

Solution steps

n = 0 \sum \infty \frac{5 n}{10 + n}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty \frac{n}{10 + n}

Apply Series Divergence Test:

diverges

= 5 diverges

= diverges

n = 0 \sum \infty 9 n^{2} - 36 n + 35

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

n = 0 \sum \infty - 8 (- \frac{2}{3})^{n}

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

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

What is the sum from n=0 to infinity of (5n)/(10+n) ?
The sum from n=0 to infinity of (5n)/(10+n) is diverges