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

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

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

n = 1 \sum \infty \frac{n}{6 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n}{6 ^{n}}

Apply Series Ratio Test:

converges

= converges

x \to 0 lim (\frac{( 1 + x ) ^{9} - 1}{x})

\frac{\partial}{\partial x} (\frac{42}{( 5 + x ^{2} + y ^{2} )})

\int \frac{1}{1 + cos ( 2 x )} d x

\int x (x^{2} + 1)^{5} d x

x = 3 y^{2}, x = 4 + 2 y^{2}

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