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""^((2n + 1))C0 - ""^((2n+ 1))C1 + ""^((...

`""^((2n + 1))C_0 - ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 - ……+""^((2n + 1))C_(2n) = `

A

0

B

1

C

`-1`

D

2

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The correct Answer is:
B
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""^((2n + 1))C_0 + ""^((2n+ 1))C_1 + ""^((2n + 1))C_2 + ……+""^((2n + 1))C_n =

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If C_(0), C_(1), C_(2), …, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then C_(0)""^(2) + 2 C_(1)""^(2) + 3C_(2)""^(2) + ...+ (n +1)C_(n)""^(2) =

If the value of (n + 2) . ""^(n)C_(0) *2^(n+1) - (n+1) * ""^(n)C_(1)*2^(n) + n* ""^(n)C_(2) * 2^(n-1) -... is equal to k(n +1) , the value of k is .

Prove the identity (1)/(""^(2n+1)C_(r)) + (1)/(""^(2n+1)C_(r+1)) = (2n+ 2)/(2n +1)*(1)/(""^(2n)C_(r))

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2m+1) 2^(n) .

Let m, in N and C_(r) = ""^(n)C_(r) , for 0 le r len Statement-1: (1)/(m!)C_(0) + (n)/((m +1)!) C_(1) + (n(n-1))/((m +2)!) C_(2) +… + (n(n-1)(n-2)….2.1)/((m+n)!) C_(n) = ((m + n + 1 )(m+n +2)…(m +2n))/((m +n)!) Statement-2: For r le 0 ""^(m)C_(r)""^(n)C_(0)+""^(m)C_(r-1)""^(n)C_(1) + ""^(m)C_(r-2) ""^(n)C_(2) +...+ ""^(m)C_(0)""^(n)C_(r) = ""^(m+n)C_(r) .

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