InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Statement-1: ` sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1)` Statement -2: ` sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)`A. 1B. 2C. 3D. 4 |
|
Answer» Correct Answer - A We have , ` sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = sum_(r =0)^(n) r. ""^(n)C_(r) x^(r)+ sum_(r =0)^(n) r. ""^(n)C_(r) x^(r)` `rArr sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = sum_(r =1 )^(n) rxx(n)/(r)xx ""^(n-1)C_(r-1) x^(r-1)xxx+ sum_(r =0)^(n) ""^(n)C_(r) x^(r)` `rArr sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) =nx sum_(r =1)^(n) ""^(n-1)C_(r-1) x^(r-1)xxx+ sum_(r =0)^(n) ""^(n)C_(r) x^(r)` `rArr sum_(r=0)^(n) (r+1)""^(n)C_(r) x^(r) = nx (1 + x)^(n-1) + 2 ^(n) (n +2)2^(n-1)` So, statement -1 is also ture ans statement-2 is a correct expanation for statement-1 . |
|