Question

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

Answer 1

Answer:

Step-by-step explanation:

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.