Saved Bookmarks
| 1. |
The value of .^(40)C_(0) xx .^(100)C_(40) - .^(40)C_(1) xx .^(99)C_(40) + .^(40)C_(2) xx .^(98)C_(40) "……." + .^(40)C_(40) xx .^(60)C_(40) is equal to "____". |
|
Answer» `=` Coefficient of `x^(40)` in `.^(40)C_(0)(1+x)^(100) - .^(40)C_(1)(1+x)^(99) + .^(40)C_(2)(1+x)^(96)+"….."+.^(40)C_(40)(1+x)^(60)` = Coefficient of `x^(40)` in `(1+x)^(60)(.^(40)C_(0)(1+x)^(40)-.^(40)C_(1)(1+x)^(39)+.^(40)C_(2)(1+x)^(38)+"....."+.^(40)C_(40))` `=` Coefficient of `x^(40)` in `(1+x)^(60)(1+x-1)^(40)` = Coefficient of `x^(40)` in `(1+x)^(60)x^(40)` `= 1` |
|