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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Ratio Test:

converges

= 5 converges

= converges

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