Calculus Examples

$\sum_{i = 1}^{5} {(\frac{2}{3})}^{i + 1}$

Step 1

Expand the series for each value of $i$ .

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

Step 2

Simplify the expanded form.

$\frac{844}{729}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{844}{729}$

Decimal Form:

$1.15775034 \dots$

Mixed Number Form:

$1 \frac{115}{729}$