Calculus Examples

$\sum_{n = 0}^{3} n!$

Step 1

Expand the series for each value of $n$ .

$0! + 1! + 2! + 3!$

Step 2

Substitute the values back and simplify $0! + 1! + 2! + 3!$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $0!$ to $1$ .

$1 + 1! + 2! + 3!$

Step 2.1.2

Expand $1!$ to $1$ .

$1 + 1 + 2! + 3!$

Step 2.1.3

Expand $2!$ to $2 \cdot 1$ .

$1 + 1 + 2 \cdot 1 + 3!$

Step 2.1.4

Multiply $2$ by $1$ .

$1 + 1 + 2 + 3!$

Step 2.1.5

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

$1 + 1 + 2 + 3 \cdot 2 \cdot 1$

Step 2.1.6

Multiply $3 \cdot 2 \cdot 1$ .

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Step 2.1.6.1

Multiply $3$ by $2$ .

$1 + 1 + 2 + 6 \cdot 1$

Step 2.1.6.2

Multiply $6$ by $1$ .

$1 + 1 + 2 + 6$

$1 + 1 + 2 + 6$

$1 + 1 + 2 + 6$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $1$ and $1$ .

$2 + 2 + 6$

Step 2.2.2

Add $2$ and $2$ .

$4 + 6$

Step 2.2.3

Add $4$ and $6$ .

$10$

$10$

$10$

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