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

The sum from n=0 to infinity of 4(2/3)^{2n} is converges

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Ratio Test:

converges

= 4 converges

= converges

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\frac{d}{d x} (sin (5 x + 2))

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\frac{d}{d x} (\frac{1}{1 + cos ( x )})

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