If `a,b,c` be in H.P. and `a gt c`, show that `(1)/(b-c) + (1)/(a-b) gt (4)/(a-c)`

If a,b,c are in H.P, where a gt c gt 0, then :

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.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 H.P., prove that ((1)/(a)+(1)/(b)-(1)/(c))((1)/(b)+(1)/(c)-(1)/(a))=(4)/(ac)-(3)/(b^(2))

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

If a,b,c are in G.P. then show that :sum{log_(a)((b)/(c))}^(-1)=-3{log_(b)((c)/(a))}^(-1)