Calculus Examples

$\sum_{n = 1}^{4} 2 n + 0.5$

Step 1

Expand the series for each value of $n$ .

$2 \cdot 1 + 0.5 + 2 \cdot 2 + 0.5 + 2 \cdot 3 + 0.5 + 2 \cdot 4 + 0.5$

Step 2

Simplify.

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Step 2.1

Multiply $2$ by $1$ .

$2 + 0.5 + 2 \cdot 2 + 0.5 + 2 \cdot 3 + 0.5 + 2 \cdot 4 + 0.5$

Step 2.2

Add $2$ and $0.5$ .

$2.5 + 2 \cdot 2 + 0.5 + 2 \cdot 3 + 0.5 + 2 \cdot 4 + 0.5$

Step 2.3

Multiply $2$ by $2$ .

$2.5 + 4 + 0.5 + 2 \cdot 3 + 0.5 + 2 \cdot 4 + 0.5$

Step 2.4

Add $4$ and $0.5$ .

$2.5 + 4.5 + 2 \cdot 3 + 0.5 + 2 \cdot 4 + 0.5$

Step 2.5

Add $2.5$ and $4.5$ .

$7 + 2 \cdot 3 + 0.5 + 2 \cdot 4 + 0.5$

Step 2.6

Multiply $2$ by $3$ .

$7 + 6 + 0.5 + 2 \cdot 4 + 0.5$

Step 2.7

Add $6$ and $0.5$ .

$7 + 6.5 + 2 \cdot 4 + 0.5$

Step 2.8

Add $7$ and $6.5$ .

$13.5 + 2 \cdot 4 + 0.5$

Step 2.9

Multiply $2$ by $4$ .

$13.5 + 8 + 0.5$

Step 2.10

Add $8$ and $0.5$ .

$13.5 + 8.5$

Step 2.11

Add $13.5$ and $8.5$ .

$22$