What is the sum from n=1 to infinity of (2^n)/(n^1) ?

The sum from n=1 to infinity of (2^n)/(n^1) is diverges

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sum from n=1 to infinity of (2^n)/(n^1)

n = 1 \sum \infty \frac{2 ^{n}}{n ^{1}}

diverges

Solution steps

n = 1 \sum \infty \frac{2 ^{n}}{n ^{1}}

Simplify

= n = 1 \sum \infty \frac{2 ^{n}}{n}

Apply Series Ratio Test:

diverges

= diverges

k = 1 \sum \infty \frac{3}{k !}

n = 1 \sum \infty \frac{3}{2 + n}

n = 1 \sum \infty \frac{n !}{( 3 n ) !}

i = 0 \sum \infty i

n = 1 \sum \infty \frac{3}{n ^{3} + n}

What is the sum from n=1 to infinity of (2^n)/(n^1) ?
The sum from n=1 to infinity of (2^n)/(n^1) is diverges