Precalculus Examples

$\sum_{k = 1}^{6} \frac{k}{k + 1}$

Step 1

Expand the series for each value of $k$ .

$\frac{1}{1 + 1} + \frac{2}{2 + 1} + \frac{3}{3 + 1} + \dots + \frac{6}{6 + 1}$

Step 2

Simplify the expanded form.

$\frac{617}{140}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{617}{140}$

Decimal Form:

$4.40714285 \dots$

Mixed Number Form:

$4 \frac{57}{140}$