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

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

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

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

3

Solution steps

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

Apply exponent rule:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

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

Apply Series Geometric Test:

3

= 3

\frac{\partial}{\partial x} (\frac{6 x}{3 x ^{2} + 4 y ^{2}})

(- 7, - 8), (0, 4)

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

2 t

t \to + 0 lim (tan (4 t))

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