Calculus Examples

$\sum_{n = 1}^{8} 3 n$

Factor $3$ out of the summation.

$(3) \sum_{n = 1}^{8} n$

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.

$(3) (\frac{8 (8 + 1)}{2})$

Simplify.

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Add $8$ and $1$ .

$3 \frac{8 \cdot 9}{2}$

Multiply $8$ by $9$ .

$3 (\frac{72}{2})$

Divide $72$ by $2$ .

$3 \cdot 36$

Multiply $3$ by $36$ .

$108$