If `a ,b ,c ,d` are in G.P., then prove that `(a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1)` are also in G.P.

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, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

If a, b, c are in A.P. then show that 3^(a), 3^(b), 3^(c) are in G.P.

If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

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, d are in G.P., then (a + b + c + d)^(2) is equal to

Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

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

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.