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 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, 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)

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 (b+c)/(a+d)= (bc)/(ad)=3 ((b-c)/(a-d)) then a,b,c,d are in (A) H.P. (B) G.P. (C) A.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 are in A.P. and a^2,b^2,c^2 are in H.P. then which of the following could and true (A) -a/2, b, c are in G.P. (B) a=b=c (C) a^3,b^3,c^3 are in G.P. (D) none of these

If a,b,c,d are conseentive binomial coefficients of (1+x)^n then (a+b)/(a), (b+c)/(b), (c+d)/(c ) are is

If a,b,c are in AP and b,c,d be in HP, then

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

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.