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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

n = 0 \sum \infty \frac{4}{n ^{2} + 1}

n = 0 \sum \infty \frac{n ^{2}}{4 ^{n}}

n = 1 \sum \infty \frac{5}{6 ^{n - 1}}

n = 0 \sum \infty \frac{n}{1 0 ^{n}}

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