Saved Bookmarks
| 1. |
If the coefficients of the rth, `(r+1)t h ,(r-2)t h`terms is the expansion of `(1+x)^(14)`are in A.P, then the largest value of `r`is. |
|
Answer» Correct Answer - 4 Coefficient of `r^(th)` and `(r+2)^(th)` terms are .^(14)C_(t-1),^(14)C_(r)` and .^(14)C_(r+1)` If these coefficients are in A.P. then `2(` .^(14)C_(r))=^(14)C_(r-1)+^(14)C_(r+1)` `implies(2(14)!)/(r!(14-r)!)=((14)!)/((r-1)!(15-r)!)+((14)!)/((r+1)!(13-r)!)` `implie3s(2(14)!)/(r!(14-r)!)+((14)![(r+1)r+(15-r)(14-r)])/((r+1)!(15-r)!)` `implies2(15-r)(r+1)=2r^(2)-28r+210` `impliesr^(2)-14r+45=0` `implies(r-5)(r-9)=0` `impliesr=5` or `9` |
|