If a,b,c are in AP, show that ` (a(b+c))/(bc) , (b (c+a))/(ca), (c(a+b))/(ab)`, are also in AP.

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

If a, b, c are in A.P., prove that : (ab+ac)/(bc), (bc+ba)/ (ca), (ca+cb)/(ab) are also in A.P.

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

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

If a, b, c are in A.P., then prove that : (i) b+c,c+a,a+b" are also in A.P." (ii) (1)/(bc),(1)/(ca),(1)/(ab)" are also in A.P." (iii) (a(b+c))/(bc),(b(c+a))/(ca),(c(a+b))/(ab)" are also in A.P."

If ab+bc+ca!=0 and a,b,c are in A.P. prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b) are also in A.P.

If a,b,c are in AP show that (i) 1/(bc) ,1/(ca),1/(ab) are in AP.

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.

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

If a^(2),b^(2) and c^(2) are in AP then prove that (a)/(b+c),(b)/(c+a) and (c)/(a+b) are also in A.P.