Algebra Examples

$\sum_{n = 1}^{6} 2 n$

Factor $2$ out of the summation.

$(2) \sum_{n = 1}^{6} n$

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

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

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

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

Simplify.

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Simplify the expression.

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Add $6$ and $1$ .

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

Multiply $6$ by $7$ .

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

$42$