What is the limit as n approaches infinity of 1/(sqrt(n^2+2n)-n) ?

The limit as n approaches infinity of 1/(sqrt(n^2+2n)-n) is 1

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limit as n approaches infinity of 1/(sqrt(n^2+2n)-n)

n \to \infty lim (\frac{1}{n ^{2} + 2 n - n})

1

Solution steps

n \to \infty lim (\frac{1}{n ^{2} + 2 n - n})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{n \to \infty} ( 1 )}{lim _{n \to \infty} ( n ^{2} + 2 n - n )}

n \to \infty lim (1) = 1

n \to \infty lim (n^{2} + 2 n - n) = 1

= \frac{1}{1}

Simplify

= 1

\frac{sec ( x )}{7 + sec ( x )}

y^{^{''}} - 36 y^{^{'}} = 0

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\int \frac{1}{x ^{2} + 1} d x

\int ((x - 2) x + 4) d x

What is the limit as n approaches infinity of 1/(sqrt(n^2+2n)-n) ?
The limit as n approaches infinity of 1/(sqrt(n^2+2n)-n) is 1