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

The sum from x=1 to infinity of (((2x)^x))/(x^{2x)} is converges

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sum from x=1 to infinity of (((2x)^x))/(x^{2x)}

x = 1 \sum \infty \frac{( ( 2 x ) ^{x} )}{x ^{2 x}}

converges

Solution steps

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

Simplify

\frac{( 2 n ) ^{n}}{n ^{2 n}} : \frac{2 ^{n}}{n ^{n}}

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

Apply exponent rule:

\frac{a ^{n}}{b ^{n}} = (\frac{a}{b})^{n}

\frac{2 ^{n}}{n ^{n}} = (\frac{2}{n})^{n}

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

Apply Series Root Test:

converges

= converges

\int \frac{2 x}{π} d x

t^{6}

y = y^{^{'}} + 2

f (x) = x^{2}, (1, 5)

\int \frac{22}{x ^{2} x ^{2} + 4} d x

What is the sum from x=1 to infinity of (((2x)^x))/(x^{2x)} ?
The sum from x=1 to infinity of (((2x)^x))/(x^{2x)} is converges