Calculus Examples

$\sum_{k = 1}^{5} 4 k$

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 and make sure to multiply by the front term.

$(4) (\frac{5 (5 + 1)}{2})$

Step 3

Simplify.

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Step 3.1

Simplify the expression.

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Step 3.1.1

Add $5$ and $1$ .

$4 \frac{5 \cdot 6}{2}$

Step 3.1.2

Multiply $5$ by $6$ .

$4 (\frac{30}{2})$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$2 (2) \frac{30}{2}$

Step 3.2.2

Cancel the common factor.

$2 \cdot 2 \frac{30}{2}$

Step 3.2.3

Rewrite the expression.

$2 \cdot 30$

Step 3.3

Multiply $2$ by $30$ .

$60$