Calculus Examples

$\sum_{i = 1}^{10} \frac{x_{i}}{12}$

Step 1

Factor $\frac{1}{12}$ out of the summation.

$\frac{1}{12} \sum_{k = 1}^{10} x_{i}$

Step 2

The formula for the summation of a constant is:

$\sum_{k = 1}^{n} c = c n$

Step 3

Substitute the values into the formula and make sure to multiply by the front term.

$\frac{1}{12} (x_{i} \cdot 10)$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $12$ .

$\frac{1}{2 (6)} (x_{i} \cdot 10)$

Step 4.1.2

Factor $2$ out of $x_{i} \cdot 10$ .

$\frac{1}{2 (6)} (2 (x_{i} \cdot 5))$

Step 4.1.3

Cancel the common factor.

$\frac{1}{2 \cdot 6} (2 (x_{i} \cdot 5))$

Step 4.1.4

Rewrite the expression.

$\frac{1}{6} (x_{i} \cdot 5)$

Step 4.2

Combine $x_{i}$ and $\frac{1}{6}$ .

$\frac{x_{i}}{6} \cdot 5$

Step 4.3

Combine $\frac{x_{i}}{6}$ and $5$ .

$\frac{x_{i} \cdot 5}{6}$

Step 4.4

Move $5$ to the left of $x_{i}$ .

$\frac{5 x_{i}}{6}$