What is the sum from n=1 to infinity of 1/n-1/(2n+1) ?

The sum from n=1 to infinity of 1/n-1/(2n+1) is diverges

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sum from n=1 to infinity of 1/n-1/(2n+1)

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

diverges

Solution steps

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

Apply Series Integral Test:

diverges

= diverges

1 - x^{2}, 0

\frac{d}{d x} (2 - 3 x^{2})

f (x) = \frac{x ^{2}}{1 + 4 x}

\int \frac{1}{( arcsin ( x ) ) ^{3} 1 - x ^{2}} d x

e^{4 (t - 3)}

What is the sum from n=1 to infinity of 1/n-1/(2n+1) ?
The sum from n=1 to infinity of 1/n-1/(2n+1) is diverges