-nr-1r-nCrn-1Cr-1 is equal to

The correct option is B n^2 given, ∑^n_r=1r.^nC_r^n 1C_r 1 = ∑^n_r=1r×n!(n r)!(r!)(n 1)!(n r)!(r 1)! #160; = ∑^n_r=1 n =n× n = n^2 ...

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Summation by Sigma Method

∑nr=1r.nCrn-1...

Question

$n \sum r = 1 \frac{r .^{n} C_{r}}{^{n - 1} C_{r - 1}}$ is equal to

\frac{n (n + 1)}{2}

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\frac{n (n - 1)}{2}

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n (n + 1)

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n^{2}

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Solution

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n

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0

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n!

r = n

n \sum r = 1 \frac{r^{n} C_{r}}{^{n} C_{r - 1}}

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