The value of - r -1 n -1- k -1 n k C r -1 where r - k - n - N is equal toA- 2 n -1B- 2n-1-1- 2n-1-2D- None of these

The correct option is C 2^n+1 2 ∑^n+1_r=1 (∑^n_k=1^kC_r 1 ) ∑^n+1_r=1 (∑^n_k=1 ( ^k+1C_r ^kC_r ) ) ∑^n+1_r=1 ( ^n+1C_r ^1C_r ) =2^n+1 2 ...

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Complex Numbers

The value of ...

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The value of $\sum_{r = 1}^{n + 1} (\sum_{k = 1}^{n}^{k} C_{r - 1})$ where r, k, n $ϵ$ N is equal to

$2^{n + 1}$

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$2^{n + 1} - 1$

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$2^{n + 1} - 2$

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None of these

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$\infty \sum n = 1 \frac{1}{(n + 1) (n + 2) (n + 3) . . . . (n + k)}$ is equal to

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\frac{C_{0}}{1 \cdot 2} 2^{2} + \frac{C_{1}}{2 \cdot 3} 2^{3} + \frac{C_{2}}{3 \cdot 4} 2^{4} + \dots + \frac{C_{n}}{(n + 1) (n + 2)} 2^{n + 2}

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p

x^{n} - 1 = 0, n > 1, n \in N,

1, a_{1}, a_{2}, \dots, a_{n - 1},

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