Question

if 1/a,1/b,1/c are in A.P so prove that b+c/a,c+a/b,a+b/c are in A.P

Answer 1

since
1/a , 1/b and 1/c are in A.P,

then

(a+b+c)/a , (a+b+c)/b and (a+b+c)/c are also in A.P,



then


[a/a + (b+c)/a], [b/b + (a+c)/b] and [c/c + (a+b)/c] are also in A.P,


hence


[1 + (b+c)/a], [1 + (a+c)/b] and [1 + (a+b)/c] are also in A.P,



therefore


(b+c)/a , (a+c)/b and (a+b)/c are also in A.P