What is the sum from k=1 to infinity} 3/(sqrt(k) of-3/(\sqrt{k+2)) ?

The sum from k=1 to infinity} 3/(sqrt(k) of-3/(\sqrt{k+2)) is 3/(sqrt(2))+3

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sum from k=1 to infinity} 3/(sqrt(k) of-3/(\sqrt{k+2))

k = 1 \sum \infty \frac{3}{k} - \frac{3}{k + 2}

\frac{3}{2} + 3

Solution steps

k = 1 \sum \infty \frac{3}{k} - \frac{3}{k + 2}

Expand telescoping series:

\frac{3}{2} + 3

= \frac{3}{2} + 3

n = 1 \sum \infty \frac{6 n}{6 n + 1}

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

k = 2 \sum \infty (- 0.95)^{k}

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

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

What is the sum from k=1 to infinity} 3/(sqrt(k) of-3/(\sqrt{k+2)) ?
The sum from k=1 to infinity} 3/(sqrt(k) of-3/(\sqrt{k+2)) is 3/(sqrt(2))+3