if a,b,c inAp prove that 1/bc,1/ca,1/ab

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If `a ,b ,c` are in A.P., prove that `1/(b c),1/(c a),1/(a b),` is also in A.P.If `a ,b ,c` are in A.P., prove that `1/(b c),1/(c a),1/(a b),` is also in A.P.
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If 1/a + 1/c + 1/(a-b) + 1/(c-b) = 0, prove that a, b, c are in HP unless b = a + c.If 1/a + 1/c + 1/(a-b) + 1/(c-b) = 0, prove that a, b, c are in HP unless b = a + c.