What is the sum from k=1 to infinity of 4/k-4/(k+1) ?

The sum from k=1 to infinity of 4/k-4/(k+1) is 4

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sum from k=1 to infinity of 4/k-4/(k+1)

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

4

Solution steps

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

Apply Telescoping Series Test:

4

= 4

n = 1 \sum \infty \frac{1}{3 n ^{2} + 8}

k = 6 \sum \infty \frac{1}{k ^{2} - 5 k + 6}

n = 2 \sum \infty \frac{1}{4 n ^{3}}

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

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

What is the sum from k=1 to infinity of 4/k-4/(k+1) ?
The sum from k=1 to infinity of 4/k-4/(k+1) is 4