If `a ,b ,c` are in A.P., then prove that the following are also in A.P. `a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)`

If a^(2),b^(2),c^(2) are in A.P.,then prove that the following are also in A.P.(i) (1)/(b+c),(1)/(c+a),(1)/(a+b) (ii) (a)/(b+c),(b)/(c+a),(c)/(a+b)

If a, b, c are in A.P. then prove that the following are also in A.P:(iii) (1)/(a)((1)/(b)+(1)/(c )),(1)/(b)((1)/(c )+(1)/(a)),(1)/(c )((1)/(a)+(1)/(b)) are in A.P

If a, b, c are in A.P. that the following are also in A.P:(i) (1)/(bc),(1)/(ca),(1)/(ab)

If a,b,c are in A.P.then prove that the following are also in A.P.(1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b))

If a,b,c are in AP , then prove that : b+c,c+a,a+b are also in AP

If a,b,c are in A.P.prove that b+c,c+a,a+b are also in A.P.