Calculus Examples

$\sum_{n = 1}^{4} (n + 1)!$

Step 1

Expand the series for each value of $n$ .

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Add $1$ and $1$ .

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

Step 2.1.2

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

$2 \cdot 1 + (2 + 1)! + (3 + 1)! + (4 + 1)!$

Step 2.1.3

Multiply $2$ by $1$ .

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

Step 2.1.4

Add $2$ and $1$ .

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

Step 2.1.5

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

$2 + 3 \cdot 2 \cdot 1 + (3 + 1)! + (4 + 1)!$

Step 2.1.6

Multiply $3 \cdot 2 \cdot 1$ .

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Step 2.1.6.1

Multiply $3$ by $2$ .

$2 + 6 \cdot 1 + (3 + 1)! + (4 + 1)!$

Step 2.1.6.2

Multiply $6$ by $1$ .

$2 + 6 + (3 + 1)! + (4 + 1)!$

$2 + 6 + (3 + 1)! + (4 + 1)!$

Step 2.1.7

Add $3$ and $1$ .

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

Step 2.1.8

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

$2 + 6 + 4 \cdot 3 \cdot 2 \cdot 1 + (4 + 1)!$

Step 2.1.9

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

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Step 2.1.9.1

Multiply $4$ by $3$ .

$2 + 6 + 12 \cdot 2 \cdot 1 + (4 + 1)!$

Step 2.1.9.2

Multiply $12$ by $2$ .

$2 + 6 + 24 \cdot 1 + (4 + 1)!$

Step 2.1.9.3

Multiply $24$ by $1$ .

$2 + 6 + 24 + (4 + 1)!$

$2 + 6 + 24 + (4 + 1)!$

Step 2.1.10

Add $4$ and $1$ .

$2 + 6 + 24 + (5)!$

Step 2.1.11

Expand $(5)!$ to $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$2 + 6 + 24 + 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$

Step 2.1.12

Multiply $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.1.12.1

Multiply $5$ by $4$ .

$2 + 6 + 24 + 20 \cdot 3 \cdot 2 \cdot 1$

Step 2.1.12.2

Multiply $20$ by $3$ .

$2 + 6 + 24 + 60 \cdot 2 \cdot 1$

Step 2.1.12.3

Multiply $60$ by $2$ .

$2 + 6 + 24 + 120 \cdot 1$

Step 2.1.12.4

Multiply $120$ by $1$ .

$2 + 6 + 24 + 120$

$2 + 6 + 24 + 120$

$2 + 6 + 24 + 120$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $2$ and $6$ .

$8 + 24 + 120$

Step 2.2.2

Add $8$ and $24$ .

$32 + 120$

Step 2.2.3

Add $32$ and $120$ .

$152$

$152$

$152$

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