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 and d are any four consecutive coefficients in the expansion of (1 + x)^(n) , then prove that (i) (a) /(a+ b) + (c)/(b+c) = (2b)/(b+c) (ii) ((b)/(b+c))^(2) gt (ac)/((a + b)(c + d)), "if " x gt 0 .

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 H.P.then prove that a+d>b+c

If a,b,c,d are any four consecutive coefficients of any expanded binomial then (a+b)/(a),(b+c)/(b),(c+d)/(c) are in

Let a,b,c,d be the foru cosecutive coefficients int eh 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 be the three consecutive coefficients in the expansion of a power oif (1+x), prove that the index power is ( 2ac+b(a+c)/(b^2-ac))