Calculus Examples

$\sum_{i = 2}^{4} x i - 5$

Step 1

Expand the series for each value of $i$ .

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

Step 2

Substitute the values back and simplify $x \cdot 2 - 5 + x \cdot 3 - 5 + x \cdot 4 - 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Move $2$ to the left of $x$ .

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

Step 2.1.2

Move $3$ to the left of $x$ .

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

Step 2.1.3

Move $4$ to the left of $x$ .

$2 x - 5 + 3 x - 5 + 4 x - 5$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $2 x$ and $3 x$ .

$5 x - 5 - 5 + 4 x - 5$

Step 2.2.2

Add $5 x$ and $4 x$ .

$9 x - 5 - 5 - 5$

Step 2.2.3

Simplify by subtracting numbers.

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Step 2.2.3.1

Subtract $5$ from $- 5$ .

$9 x - 10 - 5$

Step 2.2.3.2

Subtract $5$ from $- 10$ .

$9 x - 15$