Precalculus Examples

$\sum_{x = 1}^{6} 4 x$

Step 1

Factor $4$ out of the summation.

$(4) \sum_{x = 1}^{6} x$

Step 2

The formula for the summation of a polynomial with degree $1$ is:

$\sum_{k = 1}^{n} k = \frac{n (n + 1)}{2}$

Step 3

Substitute the values into the formula and make sure to multiply by the front term.

$(4) (\frac{6 (6 + 1)}{2})$

Step 4

Simplify.

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Step 4.1

Simplify the expression.

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Step 4.1.1

Add $6$ and $1$ .

$4 \frac{6 \cdot 7}{2}$

Step 4.1.2

Multiply $6$ by $7$ .

$4 (\frac{42}{2})$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $4$ .

$2 (2) \frac{42}{2}$

Step 4.2.2

Cancel the common factor.

$2 \cdot 2 \frac{42}{2}$

Step 4.2.3

Rewrite the expression.

$2 \cdot 42$

Step 4.3

Multiply $2$ by $42$ .

$84$