If a,b,c `in R^(+)` form an A.P then prove that a+1 /(bc) , b+1 /(ac) , c+1 /(ab) are also in A.P

If a, b, c are in A.P, prove that 1/(bc),1/(ca),1/(ab) are also in A.P.

If (b-c)^(2) , (c-a)^(2), (a-b)^(2) are in A.P. then prove that (1)/(b-c) , (1)/(c-a), (1)/(a-b) are also in A.P.

Suppose a^2,b^2,c^2 are in A.P. Prove that a/(b+c),b/(c+a),c/(a+b) are also in A.P.S

If (a)/(b+c),(b)/(c+a),(c)/(a+b) are in AP, then

Suppose a, b, c are in A.P.Prove that a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in A.P.

Suppose a, b, c are in A.P. Prove that (ab+bc+ca)/(bc),(ab+bc+ca)/(ca),(ab+bc+ca)/(ab) are in A.P.

Suppose that a, b, c are in A.P. Prove that a^2(b+c),b^2(c+a),c^2(a+b) are in A.P.

If p^(th) , q^ (th) , r^ (th) and s^ (th) terms of an A.P are in G.P , then show that (p-q),(q-r),(r-s) are also in G . P

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

If (b+c-a)/a,(c+a-b)/b,(a+b-c)/c are in A.P, prove that 1/a,1/b,1/c are also A.P.s