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

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

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

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

0

Solution steps

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

\frac{( - 1 ) ^{n + 1}}{( n + 3 ) n !} = \frac{( - 1 ) ^{n + 1}}{( n + 3 )} \cdot \frac{1}{n !}

= n \to \infty lim (\frac{( - 1 ) ^{n + 1}}{n + 3} \cdot \frac{1}{n !})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= n \to \infty lim (\frac{( - 1 ) ^{n + 1}}{n + 3}) \cdot n \to \infty lim (\frac{1}{n !})

n \to \infty lim (\frac{( - 1 ) ^{n + 1}}{n + 3}) = 0

n \to \infty lim (\frac{1}{n !}) = 0

= 0 \cdot 0

Simplify

= 0

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