What is the sum from n=1 to infinity of ((4^n+1))/(5^n) ?

The sum from n=1 to infinity of ((4^n+1))/(5^n) is converges

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sum from n=1 to infinity of ((4^n+1))/(5^n)

n = 1 \sum \infty \frac{( 4 ^{n} + 1 )}{5 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{4 ^{n} + 1}{5 ^{n}}

Apply Series Ratio Test:

converges

= converges

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

5 - x^{2}

cos (π x), at \frac{1}{2}

y = ln (3 x + 1) e^{x^{2} + 4}

\frac{( x + 7 x )}{7 x - 5}

What is the sum from n=1 to infinity of ((4^n+1))/(5^n) ?
The sum from n=1 to infinity of ((4^n+1))/(5^n) is converges