What is the sum from n=0 to infinity of 5(2/3)^{n-1} ?

The sum from n=0 to infinity of 5(2/3)^{n-1} is converges

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sum from n=0 to infinity of 5(2/3)^{n-1}

n = 0 \sum \infty 5 (\frac{2}{3})^{n - 1}

converges

Solution steps

n = 0 \sum \infty 5 (\frac{2}{3})^{n - 1}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty (\frac{2}{3})^{n - 1}

Apply Series Ratio Test:

converges

= 5 converges

= converges

x \to 0 lim (x cot (3 x))

\int \frac{3 x ^{2} + 4}{x ^{3} + 4 x} d x

\int lo g_{e} (x) d x

\frac{d}{d x} (c_{1} e^{- 4 x})

e^{- s}

What is the sum from n=0 to infinity of 5(2/3)^{n-1} ?
The sum from n=0 to infinity of 5(2/3)^{n-1} is converges