`^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

Prove that "^nC_r + 2. ^nC_(r-1) + ^nC_(r-2) = ^(n+2)C_r

Prove that ^nC_(r)+^(n-1)C_(r)+...+^(r)C_(r)=^(n+1)C_(r+1)

nC_(r):^(n)C_(r+1)=1:2 and ^(n)C_(r+1):^(n)C_(r+2)=2:3, findn and r

If (n-1)C_(r)=(k^(2)-3)nC_(r+1), then k belong to

If a_n=sum(r=0)^n 1/^nC_r, then sum _(r=0^n r/^nC_r equals (A) (n-1)a_n (B) na_n (C) 1/2na_n (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

If n is a positive integer then ^nC_r+^nC_(r+1)=^(n+1)^C_(r+1) Also coefficient of x^r in the expansion of (1+x)^n=^nC_r. In an identity in x, coefficient of similar powers of x on the two sides re equal. On the basis of above information answer the following question: If n is a positive integer then ^nC_n+^(n+1)C_n+^(n+2)C_n+.....+^(n+k)C_n= (A) ^(n+k+1)C_(n+2) (B) ^(n+k+1)C_(n+1) (C) ^(n+k+1)C_k (D) ^(n+k+1)C_(n-2)

Write the expression ^nC_(r+1)+^(n)C_(r-1)+2xx^(n)C_(r) in the simplest form.