[" 1f "a,b,c" are in "A" ."P" ,then show that "(bc)/(a(b+1c)),(ca)/(b(c+a))" ,"c(a+b)" are in "],[" H.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 show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.

If a,b,c are in H.P.show that (a-b)/(b-c)=(a)/(c)

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 (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, then show that 1/(bc) , 1/(ca) , 1/(ab) are also in A.P.

If a,b,c are in H.P.,then prove that (a)/(b+c-a),(b)/(a+b-c),(c)/(a+b-c) are in H.P.

If a,b,c are in A.P. show 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 H.P then prove that a/(b+c-a),b/(c+a-b),c/(a+b-c) are in H.P

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)