What is the sum from n=0 to infinity of ((1/3)^n)^2 ?

The sum from n=0 to infinity of ((1/3)^n)^2 is converges

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sum from n=0 to infinity of ((1/3)^n)^2

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

converges

Solution steps

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

Apply exponent rule:

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

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

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=0 to infinity of ((1/3)^n)^2 ?
The sum from n=0 to infinity of ((1/3)^n)^2 is converges