What is the sum from n=0 to infinity of 14(2/3)^n ?

The sum from n=0 to infinity of 14(2/3)^n is 42

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sum from n=0 to infinity of 14(2/3)^n

n = 0 \sum \infty 14 (\frac{2}{3})^{n}

42

Solution steps

n = 0 \sum \infty 14 (\frac{2}{3})^{n}

Apply the constant multiplication rule:

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

= 14 \cdot n = 0 \sum \infty (\frac{2}{3})^{n}

Apply Series Geometric Test:

3

= 14 \cdot 3

Simplify

= 42

k = 1 \sum \infty \frac{1}{k}

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

n = 0 \sum \infty \frac{n + 1}{2 n}

n = 3 \sum \infty \frac{1}{n ( n + 2 )}

n = 0 \sum \infty \frac{1}{ln ( n ^{2} )}

What is the sum from n=0 to infinity of 14(2/3)^n ?
The sum from n=0 to infinity of 14(2/3)^n is 42