Home
Class 12
MATHS
^nCr+^nC(r+1)+^nC(r+2) is equal to (2ler...

`^nC_r+^nC_(r+1)+^nC_(r+2)` is equal to `(2lerlen)` (A) `2^nC_(r+2)` (B) `2^(n+1)C_(r+1)` (C) `2^(n+2)C_(r+2)` (D) none of these

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

For ""^(n) C_(r) + 2 ""^(n) C_(r-1) + ""^(n) C_(r-2) =

""^(n)C_(r)+2""^(n)C_(r-1)+^(n)C_(r-2) is equal to

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=

""^(n-2)C_(r)+2""^(n-2)C_(r-1)+""^(n-2)C_(r-2) equals :

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

If C_r stands for .^nC_r and sum_(r=1)^n (r.C_r)/(C_(r-1)) =210 then n= (A) 19 (B) 20 (C) 21 (D) none of these

The value of sum_(r=1)^n(sum_(p=0)^(r-1) ^nC_r ^rC_p 2^p) is equal to (a) 4^(n)-3^(n)+1 (b) 4^(n)-3^(n)-1 (c) 4^(n)-3^(n)+2 (d) 4^(n)-3^(n)

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))

sum_(r=0)^n(-2)^r*(nC_r)/((r+2)C_r) is equal to

The value of determinant |[ ^n C_(r-1), ^n C_r, (r+1)^(n+2)C_(r+1)],[ ^n C_r, ^n C_(r+1),(r+2)^(n+2)C_(r+2)],[ ^n C_(r+1), ^n C_(r+2), (r+3)^(n+2)C_(r+3)]| is n^2+n-2 b. 0 c. ^n+3C_(r+3) d. ^n C_(r-1)+^n C_r+^n C_(r+1)