What is the sum from n=0 to infinity of 8/(5^n) ?

The sum from n=0 to infinity of 8/(5^n) is 10

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sum from n=0 to infinity of 8/(5^n)

n = 0 \sum \infty \frac{8}{5 ^{n}}

10

Solution steps

n = 0 \sum \infty \frac{8}{5 ^{n}}

Apply the constant multiplication rule:

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

= 8 \cdot n = 0 \sum \infty \frac{1}{5 ^{n}}

Apply Series Geometric Test:

\frac{5}{4}

= 8 \cdot \frac{5}{4}

Simplify

8 \cdot \frac{5}{4} : 10

= 10

(x^{3} + 9) e^{x}

\int \frac{( ( x - 2 ) ^{4} )}{4 x - x ^{2}} d x

\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}}

\frac{d}{d x} (\frac{x ^{3} + 5}{x ^{2} + 1})

t \to \infty lim (x)

What is the sum from n=0 to infinity of 8/(5^n) ?
The sum from n=0 to infinity of 8/(5^n) is 10