What is the sum from n=0 to infinity of 4(8/9)^n ?

The sum from n=0 to infinity of 4(8/9)^n is 36

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sum from n=0 to infinity of 4(8/9)^n

n = 0 \sum \infty 4 (\frac{8}{9})^{n}

36

Solution steps

n = 0 \sum \infty 4 (\frac{8}{9})^{n}

Apply the constant multiplication rule:

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

= 4 \cdot n = 0 \sum \infty (\frac{8}{9})^{n}

Apply Series Geometric Test:

9

= 4 \cdot 9

Simplify

= 36

n = 1 \sum \infty cos (n)

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

n = 0 \sum \infty n^{2} - 2

n = 0 \sum \infty \frac{5 n}{10 + n}

n = 0 \sum \infty 9 n^{2} - 36 n + 35

What is the sum from n=0 to infinity of 4(8/9)^n ?
The sum from n=0 to infinity of 4(8/9)^n is 36