InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Consider the expansion of `(1 + x)^(2n+1)` If the coefficients of `x^(r) and x^(r+1)` are equal in the expansion, then r is equal toA. nB. `(2n-1)/(2)`C. `(2n+1)/(2)`D. n + 1 |
|
Answer» Correct Answer - A `(1+x)^(2n+1)=.^((2n+1))C_(0)x^(0)+.^((2n+1))C_(1)x^(1)+...+.^((2n+1))C_(2n+1)(x)^(2n+1)` Coefficient of `x^(r)=.^((2n+1))Cr` Coefficient of `x^(r+1)=.^((2n+1))Cr + 1` `.^((2n+1))C_(r)=.^((2n+1))Cr+1` `rArr ((2n+1)!)/(r!(2n+1-r)!)=((2n+1)!)/((r+1)!(2n-r)!)` `rArr ((2n-r)!)/((2n+1-r)(2n-r)!)=(r!)/((r+1)r!)` `rArr (r + 1) = 2n + 1 - r` `rArr r = n` |
|