if the sum f an A.P is same for p and q terms, show that the sum of p+q terms is 0........
S(p+q) >0 from graph ...how can it be 0 ?????
and if S(p+q)=0 wat is the other root
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1 Answers
23S_{p} = \frac{p}{2}( 2a + [p -1]d )
S_{q} = \frac{q}{2}( 2a + [q -1]d )
S_{q} = S_{p}
q( 2a+[q-1]d) = p(2a+[p-1]d)
2a(q-p)= d(p^{2}-p-(q^{2}-q))
2a(q-p)- d(p^{2}-q^{2}-(p-q)) = 0
2a(q-p)- d((p-q)(p+q)-(p-q)) = 0
2a(q-p)+ d((q-p)(p+q)-(q-p)) = 0
2a(p+q-1)d=0
\frac{(p+q)}{2}(2a+(p+q-1)d) = 0=S_{p+q}
