- #1

psyclone

- 17

- 0

## Homework Statement

Hi All,

I found this problem,

The sum of p, q, r terms of an Arithmetic Progression, are P, Q, R respectively: show that[tex] \frac{P (q - r )}{p} + \frac{Q (r - p )}{q} + \frac{R (p - q)}{r} = 0 [/tex]

## Homework Equations

3. The Attempt at a Solution [/B]

My thoughts on how to start the problem is;

if

[tex] S_{n} = \frac{a}{2} (n + (n-1)d ) [/tex]

then the sum of say 'p' terms, would be

[tex] P = S_{p} = \frac{a}{2} (p + (p-1)d ) [/tex]

Therefore;

[tex] Q = S_{q} = \frac{a}{2} (q + (q-1)d ) [/tex][tex] R = S_{r} = \frac{a}{2} (r + (r-1)d ) [/tex]

If I used the following series, to simplify a little, [tex] S_{n} = 1 + 2 + 3 ... + n, [/tex] then [tex] S_{n} = \frac{1}{2}n(n+1) [/tex]

But how to form the above equation, which combines all series, which includes all terms (i.e p q, r, P, Q & R)?