Calculus Examples

$\sum_{n = 1}^{6} \frac{{(- 1)}^{n + 1} \cdot 4}{\ln (n + 1)}$

Step 1

Expand the series for each value of $n$ .

$\frac{{(- 1)}^{1 + 1} \cdot 4}{\ln (1 + 1)} + \frac{{(- 1)}^{2 + 1} \cdot 4}{\ln (2 + 1)} + \frac{{(- 1)}^{3 + 1} \cdot 4}{\ln (3 + 1)} + \dots + \frac{{(- 1)}^{6 + 1} \cdot 4}{\ln (6 + 1)}$

Step 2

Simplify the expanded form.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.70672273 \dots$