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If 1/a, 1/b, 1/c are in A.P. then prove that b+c/a, c+a/b, a+b/c are also in a.p.
given: 1/a , 1/b and 1/c are in APmultiplying each term by (a+b+c) will also result as an AP.(a+b+c) / a , (a+b+c)/b and (a+b+c)/c must form an APsubtracting 1 from each term is also an APtherefore(a+b+c) / a -1 , (a+b+c)/b -1 and (a+b+c)/c -1 is also an AP.therefore (b+c)/a , (a+c)/b and (a+b)/c is an AP.
given: 1/a , 1/b and 1/c are in AP
multiplying each term by (a+b+c) will also result as an AP.
(a+b+c) / a , (a+b+c)/b and (a+b+c)/c must form an AP
subtracting 1 from each term is also an AP
therefore
(a+b+c) / a -1 , (a+b+c)/b -1 and (a+b+c)/c -1 is also an AP.
therefore (b+c)/a , (a+c)/b and (a+b)/c is an AP.
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