Sum of the first p, q and r terms of an A.P are a, b and c, respectively.Prove that `a/p(q-r)+b/q(r-p)+c/r(p-q)=0`

Explanation

Let `A` is the first term and `d` is the common ratio of `AP`.
We are given,

`p/2(2A+(p-1)d) = a=>(2a)/p = (2A+(p-1)d)`

`:. (2a)/p(q-r) = (q-r)/2(2A+(p-1)d)`

`=(q-r)2A+(pq-pr)d-(q-r)d`

`:. (2a)/p(q-r) = 2A(q-r)+(pq-pr)d-(q-r)d->(1)`

Similarly,

`(2b)/q(r-p) = 2A(r-p)+(rq-pq)d-(r-p)d->(2)`

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