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))`

If a,b and c are three consecutive coefficients terms in the expansion of (1+x)^(n), then find n.

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 are any three consecutive integers, prove that log(1+ac)=2log b

If a,b,c are any three consecutive integers, prove that log(1+ac)=2log b

If some three consecutive coefficeints in the binomial expanison of (x + 1)^(n) in powers of x are in the ratio 2 : 15 : 70, then the average of these three coefficients is (A) 964 (B) 227 (C) 232 (D) 625

coefficient of a^(3)b^(2)c in the expansion of (1+a-b+c)^(9)

If a,b,c are consecutive positive integers and log(1+ac)=2K then the value of K