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

 Exercise

$\lim_{n\to\infty}\left(n-\sqrt{n^2+n}\right)$

 

Evaluate the limit $\lim_{n\to\infty }\left(n-\sqrt{n^2+n}\right)$ by replacing all occurrences of $n$ by $\infty $

$\infty -\sqrt{\infty ^2+\infty }$

 

Infinity to the power of any positive number is equal to infinity, so $\infty ^2=\infty$

$\infty -\sqrt{\infty +\infty }$

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Applying the property of infinity: $\infty+\infty=\infty$. Remember that both infinities must have the same sign

$\infty -\sqrt{\infty }$

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Infinity to the power of any positive number is equal to infinity, so $\sqrt{\infty }=\infty$

$\infty - \infty $

 

Infinity minus infinity is an indeterminate form

indeterminate

indeterminate

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