Precalculus Examples

$\sum_{i = 1}^{5} - 5 {(\frac{1}{5})}^{i - 1}$

Step 1

Expand the series for each value of $i$ .

$- 5 {(\frac{1}{5})}^{1 - 1} - 5 {(\frac{1}{5})}^{2 - 1} - 5 {(\frac{1}{5})}^{3 - 1} + \dots - 5 {(\frac{1}{5})}^{5 - 1}$

Step 2

Simplify the expanded form.

$- \frac{781}{125}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{781}{125}$

Decimal Form:

$- 6.248$

Mixed Number Form:

$- 6 \frac{31}{125}$