Calculus Examples

$\sum_{2}^{5} (n - 1)!$

Step 1

Expand the series for each value of $n$ .

$(2 - 1)! + (3 - 1)! + (4 - 1)! + (5 - 1)!$

Step 2

Substitute the values back and simplify $(2 - 1)! + (3 - 1)! + (4 - 1)! + (5 - 1)!$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Subtract $1$ from $2$ .

$(1)! + (3 - 1)! + (4 - 1)! + (5 - 1)!$

Step 2.1.2

Expand $(1)!$ to $1$ .

$1 + (3 - 1)! + (4 - 1)! + (5 - 1)!$

Step 2.1.3

Subtract $1$ from $3$ .

$1 + (2)! + (4 - 1)! + (5 - 1)!$

Step 2.1.4

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

$1 + 2 \cdot 1 + (4 - 1)! + (5 - 1)!$

Step 2.1.5

Multiply $2$ by $1$ .

$1 + 2 + (4 - 1)! + (5 - 1)!$

Step 2.1.6

Subtract $1$ from $4$ .

$1 + 2 + (3)! + (5 - 1)!$

Step 2.1.7

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

$1 + 2 + 3 \cdot 2 \cdot 1 + (5 - 1)!$

Step 2.1.8

Multiply $3 \cdot 2 \cdot 1$ .

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Step 2.1.8.1

Multiply $3$ by $2$ .

$1 + 2 + 6 \cdot 1 + (5 - 1)!$

Step 2.1.8.2

Multiply $6$ by $1$ .

$1 + 2 + 6 + (5 - 1)!$

$1 + 2 + 6 + (5 - 1)!$

Step 2.1.9

Subtract $1$ from $5$ .

$1 + 2 + 6 + (4)!$

Step 2.1.10

Expand $(4)!$ to $4 \cdot 3 \cdot 2 \cdot 1$ .

$1 + 2 + 6 + 4 \cdot 3 \cdot 2 \cdot 1$

Step 2.1.11

Multiply $4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.1.11.1

Multiply $4$ by $3$ .

$1 + 2 + 6 + 12 \cdot 2 \cdot 1$

Step 2.1.11.2

Multiply $12$ by $2$ .

$1 + 2 + 6 + 24 \cdot 1$

Step 2.1.11.3

Multiply $24$ by $1$ .

$1 + 2 + 6 + 24$

$1 + 2 + 6 + 24$

$1 + 2 + 6 + 24$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $1$ and $2$ .

$3 + 6 + 24$

Step 2.2.2

Add $3$ and $6$ .

$9 + 24$

Step 2.2.3

Add $9$ and $24$ .

$33$

$33$

$33$

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