Precalculus Examples

$\sum_{j = 0}^{4} \frac{2^{j}}{2^{j} + 1}$

Step 1

Expand the series for each value of $j$ .

$\frac{2^{0}}{2^{0} + 1} + \frac{2^{1}}{2^{1} + 1} + \frac{2^{2}}{2^{2} + 1} + \dots + \frac{2^{4}}{2^{4} + 1}$

Step 2

Simplify the expanded form.

$\frac{5809}{1530}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{5809}{1530}$

Decimal Form:

$3.79673202 \dots$

Mixed Number Form:

$3 \frac{1219}{1530}$