# Math Help - Method of difference?

1. ## Method of difference?

One formula is like this : f(r) - f(r + 1) and another is f(r) - f(r -1). Sometimes, I see them change to f(r) - f(r + 2), etc...I'm very confused. Which is which and how do I know which one to use for which question? There was one time I used f(r) - f(r + 1) and it was wrong but when I used f(r) - f(r - 1), it was correct. I've forgotten which question because it was on the net. Thanks.

2. Originally Posted by mark1950
One formula is like this : f(r) - f(r + 1) and another is f(r) - f(r -1). Sometimes, I see them change to f(r) - f(r + 2), etc...I'm very confused. Which is which and how do I know which one to use for which question? There was one time I used f(r) - f(r + 1) and it was wrong but when I used f(r) - f(r - 1), it was correct. I've forgotten which question because it was on the net. Thanks.
Hi

It depends on the question .

Example : If this is the question

$\sum^{n}_{r=1}(\frac{1}{r}-\frac{1}{r+1})$

Let $f(r)=\frac{1}{r}$ , then $f(r+1)=\frac{1}{r+1}$

So $\sum^{n}_{r=1}[f(r)-f(r+1)]$

Or if you get another question like this

$\sum^{n}_{r=1}[\frac{1}{r+1}-\frac{1}{r}]$

Then you let $f(r)=\frac{1}{r+1}$ , $f(r-1)=\frac{1}{r}$

So $\sum^{n}_{r=1}[f(r)-f(r-1)]$

Hope that helps .