What is the sum from n=0 to infinity of (2/3)^{-n} ?

The sum from n=0 to infinity of (2/3)^{-n} is diverges

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sum from n=0 to infinity of (2/3)^{-n}

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

diverges

Solution steps

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

Simplify

(\frac{2}{3})^{- n} : \frac{1}{( \frac{2}{3} ) ^{n}}

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

Simplify

\frac{1}{( \frac{2}{3} ) ^{n}} : (\frac{3}{2})^{n}

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

Apply Series Geometric Test:

diverges

= diverges

f (x) = \frac{7 ^{x}}{x ^{3}}

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

\int_{1}^{3} \frac{1}{1 + x ^{2}} d x

arctan (3 x^{2} - 1)

7 y^{^{''}} + y^{^{'}} = 0

What is the sum from n=0 to infinity of (2/3)^{-n} ?
The sum from n=0 to infinity of (2/3)^{-n} is diverges