Calculus Examples

$\sum_{i = 0}^{4} 5^{i} {(\frac{1}{3})}^{i}$

Step 1

Expand the series for each value of $i$ .

$5^{0} {(\frac{1}{3})}^{0} + 5^{1} {(\frac{1}{3})}^{1} + 5^{2} {(\frac{1}{3})}^{2} + \dots + 5^{4} {(\frac{1}{3})}^{4}$

Step 2

Simplify the expanded form.

$\frac{1441}{81}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1441}{81}$

Decimal Form:

$17.79012345 \dots$

Mixed Number Form:

$17 \frac{64}{81}$