What is the limit as n approaches infinity of n^{-3} ?

The limit as n approaches infinity of n^{-3} is 0

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limit as n approaches infinity of n^{-3}

n \to \infty lim (n^{- 3})

0

Solution steps

n \to \infty lim (n^{- 3})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= (n \to \infty lim (n))^{- 3}

Apply the common limit:

n \to \infty lim (n) = \infty

= \infty^{- 3}

Apply Infinity Property:

\infty^{- c} = 0

= 0

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What is the limit as n approaches infinity of n^{-3} ?
The limit as n approaches infinity of n^{-3} is 0