What is the sum from x=1 to infinity of x/(x(x+1)) ?

The sum from x=1 to infinity of x/(x(x+1)) is diverges

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sum from x=1 to infinity of x/(x(x+1))

x = 1 \sum \infty \frac{x}{x ( x + 1 )}

diverges

Solution steps

x = 1 \sum \infty \frac{x}{x ( x + 1 )}

Cancel the common factor:

x

= x = 1 \sum \infty \frac{1}{x + 1}

Apply Series Limit Comparison Test:

diverges

= diverges

n = 1 \sum \infty \frac{n 3 ^{n}}{n !}

k = 1 \sum \infty k e^{- 16 k}

k = 1 \sum \infty k e^{- 15 k}

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

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

What is the sum from x=1 to infinity of x/(x(x+1)) ?
The sum from x=1 to infinity of x/(x(x+1)) is diverges