Precalculus Examples

$\sum_{i = 2}^{5} 2 i - 3$

Step 1

Expand the series for each value of $i$ .

$2 \cdot 2 - 3 + 2 \cdot 3 - 3 + 2 \cdot 4 - 3 + 2 \cdot 5 - 3$

Step 2

Simplify.

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Step 2.1

Multiply $2$ by $2$ .

$4 - 3 + 2 \cdot 3 - 3 + 2 \cdot 4 - 3 + 2 \cdot 5 - 3$

Step 2.2

Subtract $3$ from $4$ .

$1 + 2 \cdot 3 - 3 + 2 \cdot 4 - 3 + 2 \cdot 5 - 3$

Step 2.3

Multiply $2$ by $3$ .

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

Step 2.4

Subtract $3$ from $6$ .

$1 + 3 + 2 \cdot 4 - 3 + 2 \cdot 5 - 3$

Step 2.5

Add $1$ and $3$ .

$4 + 2 \cdot 4 - 3 + 2 \cdot 5 - 3$

Step 2.6

Multiply $2$ by $4$ .

$4 + 8 - 3 + 2 \cdot 5 - 3$

Step 2.7

Subtract $3$ from $8$ .

$4 + 5 + 2 \cdot 5 - 3$

Step 2.8

Add $4$ and $5$ .

$9 + 2 \cdot 5 - 3$

Step 2.9

Multiply $2$ by $5$ .

$9 + 10 - 3$

Step 2.10

Subtract $3$ from $10$ .

$9 + 7$

Step 2.11

Add $9$ and $7$ .

$16$