What is the sum from n=0 to infinity}(5^{n+1 of)/(4^n(3n-1)!) ?

The sum from n=0 to infinity}(5^{n+1 of)/(4^n(3n-1)!) is converges

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sum from n=0 to infinity}(5^{n+1 of)/(4^n(3n-1)!)

n = 0 \sum \infty \frac{5 ^{n + 1}}{4 ^{n} ( 3 n - 1 ) !}

converges

Solution steps

n = 0 \sum \infty \frac{5 ^{n + 1}}{4 ^{n} ( 3 n - 1 ) !}

Apply Series Ratio Test:

converges

= converges

x \to 4 lim (- \frac{1}{x ^{\frac{3}{2}}})

\int e^{- x} 2 x d x

(4 x y + y^{2}) d x + (2 x^{2} + 2 x y) d y = 0

\frac{d y}{d x} = \frac{x - 1}{y - 1}

\int (x + 5)^{3} d x

What is the sum from n=0 to infinity}(5^{n+1 of)/(4^n(3n-1)!) ?
The sum from n=0 to infinity}(5^{n+1 of)/(4^n(3n-1)!) is converges