What is the sum from k=1 to infinity of 5/k-5/(k+1) ?

The sum from k=1 to infinity of 5/k-5/(k+1) is 5

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sum from k=1 to infinity of 5/k-5/(k+1)

k = 1 \sum \infty \frac{5}{k} - \frac{5}{k + 1}

5

Solution steps

k = 1 \sum \infty \frac{5}{k} - \frac{5}{k + 1}

Apply Telescoping Series Test:

5

= 5

n = 1 \sum \infty \frac{5}{n ( n + 1 )}

k = 1 \sum \infty \frac{4}{k}

n = 1 \sum \infty n (- \frac{3}{7})^{n}

n = 1 \sum \infty \frac{5}{n ^{2} + 36}

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

What is the sum from k=1 to infinity of 5/k-5/(k+1) ?
The sum from k=1 to infinity of 5/k-5/(k+1) is 5