If 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.

If a,b,c are in A.P.prove that: (i) (1)/(bc),(1)/(ca),(1)/(ab) are in A.P.(ii) (b+c)^(2)-a^(2),(a+c)^(2)-b^(2),(b+a)^(2)-c^(2) are in A.P.

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

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

If (a)/(b+c),(b)/(c+a),(c)/(a+b) are in A.P.and a+b+c!=0 prove that (1)/(b+c),(1)/(c+a),(1)/(a+b) are in A.P.

If 1/a,1/b,1/c are in A.P. prove that: (i) (b+c)/a,(c+a)/b,(a+b)/c are also in A.P. (ii) a(b+c),b(c+a),c(a+b) are also in A.P.

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

"If " a^(2), b^(2), c^(2)" are in A.P., prove that "(1)/(b+c),(1)/(c+a),(1)/(a+b) " 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.

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