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 are in A.P., prove that 1/(b c),1/(c a),1/(a b), is 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 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 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 (b+c-a)/(a) , (c+a-b)/(b) , (a+b-c)/(c) are in A.P. then prove that (1)/(a),(1)/(b),(1)/(c) 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), b (c+a) , c (a +b) are in A.P. , prove that (1)/(a), (a)/(b), (1)/(c ) are also ln A.P.

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(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 ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(1//a c),c+1//(a b) are also in A.P.