Calculus Examples

$\sum_{k = 1}^{6} 5 k$

Step 1

Factor $5$ out of the summation.

$(5) \sum_{k = 1}^{6} k$

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.

$(5) (\frac{6 (6 + 1)}{2})$

Step 4

Simplify.

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Step 4.1

Add $6$ and $1$ .

$5 \frac{6 \cdot 7}{2}$

Step 4.2

Multiply $6$ by $7$ .

$5 (\frac{42}{2})$

Step 4.3

Divide $42$ by $2$ .

$5 \cdot 21$

Step 4.4

Multiply $5$ by $21$ .

$105$