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

The sum from n=1 to infinity} 2/(sqrt(n) of-2/(\sqrt{n+1)) is 2

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sum from n=1 to infinity} 2/(sqrt(n) of-2/(\sqrt{n+1))

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

2

Solution steps

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

Apply Telescoping Series Test:

2

= 2

\int \frac{x ^{2}}{( 1 - x ^{2} ) ^{\frac{5}{2}}} d x

\frac{e ^{- 2 s}}{s ^{2}}

x \to - 2 lim (8)

f (x) = \frac{168}{( x + 4 ) ^{5}}

f (x) = x e^{x}

What is the sum from n=1 to infinity} 2/(sqrt(n) of-2/(\sqrt{n+1)) ?
The sum from n=1 to infinity} 2/(sqrt(n) of-2/(\sqrt{n+1)) is 2