What is the sum from n=0 to infinity of 9(5/12)^n ?

The sum from n=0 to infinity of 9(5/12)^n is 108/7

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sum from n=0 to infinity of 9(5/12)^n

n = 0 \sum \infty 9 (\frac{5}{12})^{n}

\frac{108}{7}

Decimal

15.42857 \dots

Solution steps

n = 0 \sum \infty 9 (\frac{5}{12})^{n}

Apply the constant multiplication rule:

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

= 9 \cdot n = 0 \sum \infty (\frac{5}{12})^{n}

Apply Series Geometric Test:

\frac{12}{7}

= 9 \cdot \frac{12}{7}

Simplify

9 \cdot \frac{12}{7} : \frac{108}{7}

= \frac{108}{7}

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

a re a y = sin (x), y = cos (x), x = \frac{5 π}{4}, x = 2 π

t an g e n t y = \frac{2 x}{x + 2}, (2, 1)

\frac{d}{d x} ((4^{x})^{9})

x \to \infty + lim (\frac{1}{0})

What is the sum from n=0 to infinity of 9(5/12)^n ?
The sum from n=0 to infinity of 9(5/12)^n is 108/7