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Chapter 8: Problem 27

Evaluate each factorial expression. $$\frac{(n+2) !}{n !}$$

Short Answer

Expert verified
The simplified form of \(\frac{(n+2) !}{n !}\) is \((n+2) \cdot (n+1)\)

Step by step solution

01

Expand the Factorial in the Numerator

The factorial operation expands a number into the product of all integers from one to that number. Expanding (n+2)! We can write it as \((n+2) \cdot (n+1) \cdot n!\)
02

Simplify the Expression

The expression now becomes \(\frac{(n+2) \cdot (n+1) \cdot n!}{n !}\). Noticing that there is a \(n!\) both in the numerator and the denominator, these will cancel out.
03

Final Simplification

After simplification, the final expression is \((n+2) \cdot (n+1)\). This is a simplified form of the given factorial expression.

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