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

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

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

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

n = 8 \sum \infty \frac{1}{n ^{2} + 64}

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

n = 1 \sum \infty \frac{n e ^{n}}{n !}

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

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

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