If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) `(a+b)/a , (b+c)/b , (c+d)/c` are in H.P. (ii) `(bc + ad) (b-c) = 2(ac^2 - b^2d)`

If the four consecutive coefficients in any binomial expansion be a,b,c and d then (A) (a+b)/a,(b+c)/b,(c+d)/c are in H.P. (B) (bc+ad)(b-c)=2(ac^2-b^2d) (C) b/a,c/b,d/c are in A.P. (D) none of these

If a,b,c,d………are in G.P., then show that (a+b)^2, (b+c)^2, (c+d)^2 are in G.P.

If a,b,c,d………are in G.P., then show that (a-b)^2, (b-c)^2, (c-d)^2 are in G.P.

If a ,b,c , d are in G.P. prove that (b + c)(b + d) = (c + a)(c+d)

If a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^(n) , then value of the expression (((b)/(b+c))^(2)-(ac)/((a+b)(c+d))) (where x gt 0 and n in N ) is

Let a,b,c,d be the four consecutive coefficients of the binomial expansion (1+x)^n On the basis of above information answer the following question: a/(a+b), b/(b+c), c/(c+d) are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

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

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

If a, b, c, d are in G.P., prove that a^(2) - b^(2), b^(2)-c^(2), c^(2)-d^(2) are also in G.P.

A ,\ B ,\ C ,\ D are four consecutive points on a circle such that A B=C Ddot Prove that A C=B D