What is the sum from n=0 to infinity of 9(2/3)^n ?

The sum from n=0 to infinity of 9(2/3)^n is 27

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sum from n=0 to infinity of 9(2/3)^n

n = 0 \sum \infty 9 (\frac{2}{3})^{n}

27

Solution steps

n = 0 \sum \infty 9 (\frac{2}{3})^{n}

Apply the constant multiplication rule:

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

= 9 \cdot n = 0 \sum \infty (\frac{2}{3})^{n}

Apply Series Geometric Test:

3

= 9 \cdot 3

Simplify

= 27

\frac{d y}{d t} = 9 y - y^{2} - \frac{81}{4}

\frac{d}{d a} (sin^{4} (a) - cos^{4} (a) + 2 cos^{2} (a))

\int \frac{sin ( 2 x )}{1 + cos ^{4} ( x )} d x

y = \frac{x + 1}{x}

x \to - 87 lim (F (x))

What is the sum from n=0 to infinity of 9(2/3)^n ?
The sum from n=0 to infinity of 9(2/3)^n is 27