What is the sum from n=1 to infinity of 5/(n(n+6)) ?

The sum from n=1 to infinity of 5/(n(n+6)) is converges

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sum from n=1 to infinity of 5/(n(n+6))

n = 1 \sum \infty \frac{5}{n ( n + 6 )}

converges

Solution steps

n = 1 \sum \infty \frac{5}{n ( n + 6 )}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{n ( n + 6 )}

Apply Series Comparison Test:

converges

= 5 converges

= converges

2 x^{2} + 3 x y + 1 y^{3} = - 10, (- 3, - 4)

x^{2} y^{^{''}} + x y^{^{'}} + y = sec (ln (x))

\frac{d}{d x} (\frac{x + 2}{x - 3})

\frac{d}{d x} (ln^{3} (3 x^{2} - 5))

\int (x^{2} + 2)^{3} d x

What is the sum from n=1 to infinity of 5/(n(n+6)) ?
The sum from n=1 to infinity of 5/(n(n+6)) is converges