What is the sum from n=0 to infinity of 2/(5^n) ?

The sum from n=0 to infinity of 2/(5^n) is 5/2

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sum from n=0 to infinity of 2/(5^n)

n = 0 \sum \infty \frac{2}{5 ^{n}}

\frac{5}{2}

Solution steps

n = 0 \sum \infty \frac{2}{5 ^{n}}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{1}{5 ^{n}}

Apply Series Geometric Test:

\frac{5}{4}

= 2 \cdot \frac{5}{4}

Simplify

2 \cdot \frac{5}{4} : \frac{5}{2}

= \frac{5}{2}

\frac{d}{d x} (csc (2 x))

\frac{d y}{d x} = - \frac{x}{4 y}

\frac{\partial}{\partial y} (8 x y^{2} z^{3})

\int_{0}^{2} sin (x) d x

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

What is the sum from n=0 to infinity of 2/(5^n) ?
The sum from n=0 to infinity of 2/(5^n) is 5/2