If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP, prove that a,b,c are in AP | Sequence |Series

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If a `(1/b+1/c),b(1/c+1/a),c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.... If a `(1/b+1/c),b(1/c+1/a),c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P....
If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P., prove that a, b, c are in A.P. If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P., prove that a, b, c are in A.P.
if a(1/b + 1/c) , b (1/c + 1/a) , c (1/a + 1/b ) are in AP ., prove that a,b,c are in AP. if a(1/b + 1/c) , b (1/c + 1/a) , c (1/a + 1/b ) are in AP ., prove that a,b,c are in AP.
If a `(1/b+1/c),b(1/c+1/a),c(1/a+1/b)`are in A.P., prove that a, b, c are in A.P. If a `(1/b+1/c),b(1/c+1/a),c(1/a+1/b)`are in A.P., prove that a, b, c are in A.P.
"If `1/a ,1/b ,1/c`are in A.P. prove that: `(b+c)/a ,(c+a)/b ,(a+b)/c`are in A.P." "If `1/a ,1/b ,1/c`are in A.P. prove that: `(b+c)/a ,(c+a)/b ,(a+b)/c`are in A.P."
If 1/a, 1/b, 1/c are in A.P., prove that: a(b+c), b(c+a), c(a+b) are in A.P. If 1/a, 1/b, 1/c are in A.P., prove that: a(b+c), b(c+a), c(a+b) are in A.P.
If (b+c-a)/a, (c+a-b)/b, (a+b-c)/c are in AP Prove that 1/a, 1/b, 1/c are AP |Arithmetic Progression If (b+c-a)/a, (c+a-b)/b, (a+b-c)/c are in AP Prove that 1/a, 1/b, 1/c are AP |Arithmetic Progression
If `(1)/(b+c),(1)/(c+a),(1)/(a+b)` are in A.P., then If `(1)/(b+c),(1)/(c+a),(1)/(a+b)` are in A.P., then