What is the limit as n approaches infinity of 1/(3^{n-1)} ?

The limit as n approaches infinity of 1/(3^{n-1)} is 0

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limit as n approaches infinity of 1/(3^{n-1)}

n \to \infty lim (\frac{1}{3 ^{n - 1}})

0

Solution steps

n \to \infty lim (\frac{1}{3 ^{n - 1}})

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} ( 3 ^{n - 1} )}

n \to \infty lim (1) = 1

n \to \infty lim (3^{n - 1}) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to \infty lim (e^{x} - e x)

x \to - \infty lim (\frac{4 x ^{2} + 5 x}{x})

x \to 0 lim (2 - 6 x + 4 x^{2})

x \to 3 lim (\frac{x - 1}{x ^{2} + 1})

x \to 0 lim (\frac{4}{sin ( x )})

What is the limit as n approaches infinity of 1/(3^{n-1)} ?
The limit as n approaches infinity of 1/(3^{n-1)} is 0