If `a ,b ,a n dc` are in G.P. then prove that `1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot`

If a, b, c are in G.P., then prove that (1)/(a^(2)-b^(2))-(1)/(b^(2)-c^(2))=-(1)/(b^(2)) . [Hint : Put b = ar, c = ar^(2) ]

If a, b, c, d are in GP, then prove that 1/((a^(2)+b^(2))), 1/((b^(2)+c^(2))), 1/((c^(2)+d^(2))) are in GP.

If a,b,c are in G.P., then show that : (a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2)

If a,b,c are in G.P.then prove that (a^(2)+ab+b^(2))/(bc+ca+ab)=(b+a)/(c+b)

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

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

If a, b, c are in geometric progression, then prove that : (1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))

If a, b, c are in GP, prove that 1/((a+b)), 1/(2b), 1/(b+c) are in AP.

If a,b,c,d are in G.P.,prove that (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.and (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P

If a,b,c,d are in G.P.prove that: (i) quad (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P. (i) (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.