InterviewSolution
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InterviewSolution
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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`) isA. positiveB. negativeC. zeroD. depends on `n` |
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Answer» Correct Answer - A `(a)` `a=^(n)C_(r-1)`, `b=^(n)C_(r )`, `c=^(n)C_(r+1)`, `d=^(n)C_(r+2)` `a+b=^(n+1)C_(r )` `b+c=^(n+1)C_(r+1)` `c+d=^(n+1)C_(r+2)` `(a+b)/(a)=(n+1)/(r )` `implies(a)/(a+b)=(r )/(n+1)`, `(b)/(b+c)=(r+1)/(n+1)`, `(c )/(c+d)=(r+2)/(n+1)` `:. (a)/(a+b)`, `(b)/(b+c)`, `(c )/(c+d)` are in `A.P.` `A.M. gt G. M.` `(b)/(b+c) gt sqrt((ac)/((a+b)(c+d)))` `implies((b)/(b+c))^(2)-(ac)/((a+b)(c+d)) gt 0` |
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