What is the sum from n=10 to infinity of 2/3 (3/4)^n ?

The sum from n=10 to infinity of 2/3 (3/4)^n is converges

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sum from n=10 to infinity of 2/3 (3/4)^n

n = 10 \sum \infty \frac{2}{3} (\frac{3}{4})^{n}

converges

Solution steps

n = 10 \sum \infty \frac{2}{3} (\frac{3}{4})^{n}

Apply the constant multiplication rule:

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

= \frac{2}{3} \cdot n = 10 \sum \infty (\frac{3}{4})^{n}

Apply Series Ratio Test:

converges

= \frac{2}{3} converges

= converges

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What is the sum from n=10 to infinity of 2/3 (3/4)^n ?
The sum from n=10 to infinity of 2/3 (3/4)^n is converges