Calculus Examples

$\sum_{n = 1}^{8} \frac{{(- 1)}^{n + 1}}{n \ln (n)}$

Step 1

Expand the series for each value of $n$ .

$\frac{{(- 1)}^{1 + 1}}{1 \ln (1)} + \frac{{(- 1)}^{2 + 1}}{2 \ln (2)} + \frac{{(- 1)}^{3 + 1}}{3 \ln (3)} + \dots + \frac{{(- 1)}^{8 + 1}}{8 \ln (8)}$

Step 2

Simplify the expanded form.

$\frac{{(- 1)}^{1 + 1}}{0} + \frac{{(- 1)}^{2 + 1}}{2 \ln (2)} + \frac{{(- 1)}^{3 + 1}}{3 \ln (3)} + \frac{{(- 1)}^{4 + 1}}{4 \ln (4)} + \frac{{(- 1)}^{5 + 1}}{5 \ln (5)} + \frac{{(- 1)}^{6 + 1}}{6 \ln (6)} + \frac{{(- 1)}^{7 + 1}}{7 \ln (7)} + \frac{{(- 1)}^{8 + 1}}{8 \ln (8)}$

Step 3

The expression contains a division by $0$ . The expression is undefined.

Undefined