Solution: Step 1: First, we need to understand what 2 (2 factorial) means. The factorial of a number is the product of all positive integers up to that number. Therefore, 2 = 2 times 1. Step 2: Now, we calculate the reciprocal of 2. The reciprocal of a number is 1 divided by that number. So we have frac12 which simplifies to frac12 times 1. Step 3: Finally, we simplify the fraction by performing the multiplication in the denominator. We get frac12, which is the exact form. This can also be expressed as a decimal, which is 0.5. Knowledge Notes: The factorial of a number n, denoted as n, is the product of all positive integers less than or equal to n. For example: - 1 = 1 - 2 = 2 times 1 = 2 - 3 = 3 times 2 times 1 = 6 - And so on... The factorial function is defined only for non-negative integers. The reciprocal of a number is simply one divided by that number. For example, the reciprocal of 5 is frac15. When evaluating expressions involving factorials and their reciprocals, it is often helpful to simplify the factorial first and then take the reciprocal to make the calculation easier. In mathematics, it is common to express numbers in their exact form (as fractions) and their decimal form. The exact form of a number is its representation as a fraction, while the decimal form is its representation as a decimal number, which can be finite or infinite and repeating.

Evaluate 1/2!

The problem is asking for the evaluation of the mathematical expression 1/2!, where "!" denotes the factorial operation. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. The task involves calculating the factorial of 2 and then taking the reciprocal of that value to arrive at the answer for 1/2!.

$\frac{1}{2} !$

Answer

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Solution:

Step 1:

First, we need to understand what $2!$ (2 factorial) means. The factorial of a number is the product of all positive integers up to that number. Therefore, $2! = 2 \times 1$.

Step 2:

Now, we calculate the reciprocal of $2!$. The reciprocal of a number is $1$ divided by that number. So we have $\frac{1}{2!}$ which simplifies to $\frac{1}{2 \times 1}$.

Step 3:

Finally, we simplify the fraction by performing the multiplication in the denominator. We get $\frac{1}{2}$, which is the exact form. This can also be expressed as a decimal, which is $0.5$.

Knowledge Notes:

The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n. For example:

$1! = 1$
$2! = 2 \times 1 = 2$
$3! = 3 \times 2 \times 1 = 6$
And so on...

The factorial function is defined only for non-negative integers.

The reciprocal of a number is simply one divided by that number. For example, the reciprocal of 5 is $\frac{1}{5}$.

When evaluating expressions involving factorials and their reciprocals, it is often helpful to simplify the factorial first and then take the reciprocal to make the calculation easier.

In mathematics, it is common to express numbers in their exact form (as fractions) and their decimal form. The exact form of a number is its representation as a fraction, while the decimal form is its representation as a decimal number, which can be finite or infinite and repeating.