Calculus Examples

$\sum_{k = 1}^{13} k$

Step 1

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

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

Step 2

Substitute the values into the formula.

$\frac{13 (13 + 1)}{2}$

Step 3

Simplify.

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Step 3.1

Add $13$ and $1$ .

$\frac{13 \cdot 14}{2}$

Step 3.2

Multiply $13$ by $14$ .

$\frac{182}{2}$

Step 3.3

Divide $182$ by $2$ .

$91$