Manipal MET2021MathematicsBinomial Theorem
The value of C(n, 2) (n+1)! is
Options
- A1 2 e+1
- Be+1
- C1 2 e-1
- De
Correct answer
C. 1 2 e-1
Step-by-step solution
Now, ^n C₂ (n+1)! = n! (n-2)!2! ( +1)! aligned & = n! 2(n+1)!(n-2)! = n(n-1) 2(n+1)! & = n^2-1+1-n 2(n+1)! & = 1 2 [ (n-7) n! - 1 n! + 2 (n+1)! ] & = 1 2 [ 1 (n-1)! - 2 n! + 2 (n+1)! ] aligned Put n=0,1,2,3, , we get aligned & = 1 2 [e-2(e)+2(e-1)] & = 1 2 [e-2]= e 2 -1 aligned