- #1

thomas49th

- 655

- 0

**Method of differences exam question [urgent]**

## Homework Statement

[tex]\sum^{n}_{r=1}{\frac{5r+4}{r(r+1)(r+2)}[/tex]

Now i know that this is equal to [tex]\frac{2}{r} + \frac{1}{r+1} -\frac{3}{r+2}[/tex]

I need to use the method of differences to work out the summation of the series from 1 to n.

so i substitute values in

r=1:

[tex]2 + \frac{1}{2} - \frac{3}{3}[/tex]

r=2:

[tex]1 + \frac{1}{3} - \frac{3}{4}[/tex]

r=3:

[tex]\frac{2}{3} + \frac{1}{4} - \frac{3}{5}[/tex]

r=n-1:

[tex]\frac{2}{n-1} + \frac{1}{n} - \frac{3}{n+1}[/tex]

r=n:

[tex]\frac{2}{n} + \frac{1}{n+1} - \frac{3}{n+2}[/tex]But I can't see any terms that have canceled out. How do i simplify this

Thanks :)

Thomas