What is the sum from n=0 to infinity of 10(3/4)^n ?

The sum from n=0 to infinity of 10(3/4)^n is 40

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sum from n=0 to infinity of 10(3/4)^n

n = 0 \sum \infty 10 (\frac{3}{4})^{n}

40

Solution steps

n = 0 \sum \infty 10 (\frac{3}{4})^{n}

Apply the constant multiplication rule:

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

= 10 \cdot n = 0 \sum \infty (\frac{3}{4})^{n}

Apply Series Geometric Test:

4

= 10 \cdot 4

Simplify

= 40

n = 0 \sum \infty \frac{1}{2 ^{3 n}}

n = 0 \sum \infty \frac{5}{1 0 ^{n}}

k = 1 \sum \infty \frac{k}{ln ( k )}

n = 1 \sum \infty \frac{7 ^{n}}{n ! n}

n = 0 \sum \infty 8 (\frac{1}{9})^{n}

What is the sum from n=0 to infinity of 10(3/4)^n ?
The sum from n=0 to infinity of 10(3/4)^n is 40