Precalculus Examples

$\sum_{x = 1}^{5} x (x + 1)$

Step 1

Simplify the summation.

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Step 1.1

Apply the distributive property.

$x \cdot x + x \cdot 1$

Step 1.2

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1$

Step 1.3

Multiply $x$ by $1$ .

$x^{2} + x$

Step 1.4

Rewrite the summation.

$\sum_{x = 1}^{5} x^{2} + x$

Step 2

Expand the series for each value of $x$ .

$1^{2} + 1 + 2^{2} + 2 + 3^{2} + 3 + \dots + 5^{2} + 5$

Step 3

Simplify the expanded form.

$70$