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

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

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

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

converges

Solution steps

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

Simplify

= n = 1 \sum \infty (\frac{6}{n})^{n}

Apply Series Root Test:

converges

= converges

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

n = 1 \sum \infty \frac{17 n}{n !}

n = 9 \sum \infty \frac{n !}{n ^{n}}

n = 0 \sum \infty cos (5 n) π

x = 0 \sum \infty ln (x)

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