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

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

(a) If a^(2)+2bc,b^(2)+2ac,c^(2)+2ab are in A.P ., show that (1)/(b-c),(1)/(c-a),(1)/(a-b) are in A.P . (b) Prove that the sum to n terms of the series 11+103+1005+…. = (10)/(9)(10^(n)-1)+n^(2) .

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/(b c),1/(c a),1/(a b), is 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., 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 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, 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.