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

If a,b,c are in A.P. prove that the following are also in A.P. b+c, c+a, a+b

If a ,b ,c are in A.P., then prove that the following are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b)

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

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

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

If a,b,c are in A.P. prove that the following are also in A.P. a^(2)(b+c) , b^(2) (c+a) , c^(2)(a+b)

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

If a ,b ,c are in A.P., prove that the following are also in A.P. (i) 1/(b c),1/(c a),1/(a b), (ii) b+c ,c+a ,a+b (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) (iv) a^2(b+c),b^2(c+a),c^2(a+b) (v) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

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,b,c are in A.P. prove that b+c,c+a,a+b are also in A.P.