What is the limit as x approaches 3 of (x!)/((x+1)!) ?

The limit as x approaches 3 of (x!)/((x+1)!) is 1/4

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limit as x approaches 3 of (x!)/((x+1)!)

x \to 3 lim (\frac{x !}{( x + 1 ) !})

\frac{1}{4}

Decimal Notation

0.25

Solution steps

x \to 3 lim (\frac{x !}{( x + 1 ) !})

Plug in the value

x = 3

= \frac{3 !}{( 3 + 1 ) !}

Simplify

\frac{3 !}{( 3 + 1 ) !} : \frac{1}{4}

= \frac{1}{4}

x \to 3 lim (x^{2} - x - 7)

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

x \to 3 lim ((\frac{6}{3})^{x})

x \to 3 lim (x^{2} + x - 6)

x \to 3 lim ((2 - x) e^{x})

What is the limit as x approaches 3 of (x!)/((x+1)!) ?
The limit as x approaches 3 of (x!)/((x+1)!) is 1/4