What is the sum from n=0 to infinity of (2/3)(5/4)^n ?

The sum from n=0 to infinity of (2/3)(5/4)^n is diverges

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sum from n=0 to infinity of (2/3)(5/4)^n

n = 0 \sum \infty (\frac{2}{3}) (\frac{5}{4})^{n}

diverges

Solution steps

n = 0 \sum \infty \frac{2}{3} (\frac{5}{4})^{n}

Apply the constant multiplication rule:

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

= \frac{2}{3} \cdot n = 0 \sum \infty (\frac{5}{4})^{n}

Apply Series Geometric Test:

diverges

= \frac{2}{3} diverges

= diverges

e^{- 2 s} \frac{1}{( s + 1 ) ^{2}}

y^{^{'}} = \frac{x ^{2}}{y}

\int \frac{8}{( x - 2 ) ( x ^{2} + 4 )} d x

\int e^{6 x} - 4 d x

\int \frac{y}{x ^{2} + 1} d x

What is the sum from n=0 to infinity of (2/3)(5/4)^n ?
The sum from n=0 to infinity of (2/3)(5/4)^n is diverges