Calculus Examples

$\sum_{i = 5}^{9} \frac{i}{x + i}$

Step 1

Expand the series for each value of $i$ .

$\frac{5}{x + 5} + \frac{6}{x + 6} + \frac{7}{x + 7} + \dots + \frac{9}{x + 9}$

Step 2

Simplify the expanded form.

$\frac{35 x^{4} + 970 x^{3} + 9975 x^{2} + 45096 x + 75600}{(x + 5) (x + 6) (x + 7) (x + 8) (x + 9)}$