What is the sum from n=0 to infinity of (5/4)(2/3)^n ?

The sum from n=0 to infinity of (5/4)(2/3)^n is 15/4

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sum from n=0 to infinity of (5/4)(2/3)^n

n = 0 \sum \infty (\frac{5}{4}) (\frac{2}{3})^{n}

\frac{15}{4}

Solution steps

n = 0 \sum \infty \frac{5}{4} (\frac{2}{3})^{n}

Apply the constant multiplication rule:

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

= \frac{5}{4} \cdot n = 0 \sum \infty (\frac{2}{3})^{n}

Apply Series Geometric Test:

3

= \frac{5}{4} \cdot 3

Simplify

\frac{5}{4} \cdot 3 : \frac{15}{4}

= \frac{15}{4}

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

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

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

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}})

x - x^{3}

What is the sum from n=0 to infinity of (5/4)(2/3)^n ?
The sum from n=0 to infinity of (5/4)(2/3)^n is 15/4