What is the sum from n=0 to infinity of 7/n-7/(n+1) ?

The sum from n=0 to infinity of 7/n-7/(n+1) is 7

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sum from n=0 to infinity of 7/n-7/(n+1)

n = 0 \sum \infty \frac{7}{n} - \frac{7}{n + 1}

7

Solution steps

n = 1 \sum \infty \frac{7}{n} - \frac{7}{n + 1}

Apply Telescoping Series Test:

7

= 7

n = 1 \sum \infty (\frac{4}{5})^{n + 1}

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

n = 0 \sum \infty \frac{1}{( 1 - n ) ^{3}}

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

n = 1 \sum \infty \frac{8}{n ( n + 3 )}

What is the sum from n=0 to infinity of 7/n-7/(n+1) ?
The sum from n=0 to infinity of 7/n-7/(n+1) is 7