Algebra Examples

$a_{n} = \frac{n}{(n + 1)!}$

Step 1

Substitute in the value of $n$ to find the $n$ th term.

$a_{2} = \frac{2}{((2) + 1)!}$

Step 2

Simplify the denominator.

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Step 2.1

Add $2$ and $1$ .

$a_{2} = \frac{2}{(3)!}$

Step 2.2

Expand $(3)!$ to $3 \cdot 2 \cdot 1$ .

$a_{2} = \frac{2}{3 \cdot 2 \cdot 1}$

Step 2.3

Multiply $3 \cdot 2 \cdot 1$ .

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Step 2.3.1

Multiply $3$ by $2$ .

$a_{2} = \frac{2}{6 \cdot 1}$

Step 2.3.2

Multiply $6$ by $1$ .

$a_{2} = \frac{2}{6}$

$a_{2} = \frac{2}{6}$

$a_{2} = \frac{2}{6}$

Step 3

Cancel the common factor of $2$ and $6$ .

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Step 3.1

Factor $2$ out of $2$ .

$a_{2} = \frac{2 (1)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6$ .

$a_{2} = \frac{2 \cdot 1}{2 \cdot 3}$

Step 3.2.2

Cancel the common factor.

$a_{2} = \frac{2 \cdot 1}{2 \cdot 3}$

Step 3.2.3

Rewrite the expression.

$a_{2} = \frac{1}{3}$

$a_{2} = \frac{1}{3}$

$a_{2} = \frac{1}{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$