Calculus Examples

$\sum_{k = 1}^{12} k$

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.

$\frac{12 (12 + 1)}{2}$

Simplify.

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Cancel the common factor of $12$ and $2$ .

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Factor $2$ out of $12 (12 + 1)$ .

$\frac{2 (6 (12 + 1))}{2}$

Cancel the common factors.

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Factor $2$ out of $2$ .

$\frac{2 (6 (12 + 1))}{2 (1)}$

Cancel the common factor.

$\frac{2 (6 (12 + 1))}{2 \cdot 1}$

Rewrite the expression.

$\frac{6 (12 + 1)}{1}$

Divide $6 (12 + 1)$ by $1$ .

$6 (12 + 1)$

Simplify the expression.

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Add $12$ and $1$ .

$6 \cdot 13$

Multiply $6$ by $13$ .

$78$