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![[Post New]](/templates/default/images/icon_minipost_new.gif) 6 Dec 2007 12:47:39 IST
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1/a, 1/b, 1/c, 1/d r in ap
1/b - 1/a = 1/c-1/b = 1/d-1/c=(1/d-1/a)/3
or (a-b)/ab = (b-c)/bc=(c-d)/cd=(a-d)/3ad = k(say)
a-b = kab, b-c=kbc,c-d=kcd,a-d=3kad
(a-b)+(b-c)+(c-d)-(a-d) = k(ab+bc+cd-3ad) =0
so ab+bc+cd=3ad
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