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

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

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

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

n = 1 \sum \infty \frac{1}{7 ^{n - 1}}

n = 1 \sum \infty ln (1 + n)

n = 0 \sum \infty (\frac{5 π}{e})^{n}

n = 1 \sum \infty \frac{( 2 n ) !}{n !}

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

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