What is the sum from n=0 to infinity of ((2^n))/(9^{2n+1)} ?

The sum from n=0 to infinity of ((2^n))/(9^{2n+1)} is converges

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sum from n=0 to infinity of ((2^n))/(9^{2n+1)}

n = 0 \sum \infty \frac{( 2 ^{n} )}{9 ^{2 n + 1}}

converges

Solution steps

n = 0 \sum \infty \frac{2 ^{n}}{9 ^{2 n + 1}}

Apply Series Ratio Test:

converges

= converges

\int 2 x^{2} - 3 x + 2 d x

x \to π lim (sin (\frac{x}{2}))

\frac{d}{d x} (x^{\frac{4}{3}} + e^{- 5 x})

y^{^{''}} + 18 y^{^{'}} + 81 y = 0

\int_{0}^{\frac{3 π}{2}} cos^{3} (25 x) d x

What is the sum from n=0 to infinity of ((2^n))/(9^{2n+1)} ?
The sum from n=0 to infinity of ((2^n))/(9^{2n+1)} is converges