If Cr=.nCr then prove that (C0+C1)(C1+C2)…..(Cn−1+Cn)=(C1C2….Cn−1Cn)(n+1)n/n!

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If {C}_{{{r}}}=.^{{{n}}}{C}_{{{r}}} then prove that {({C}_{{{0

Question

If $C_{r} = .^{n} C_{r}$ then prove that $(C_{0} + C_{1}) (C_{1} + C_{2}) \dots .. (C_{n - 1} + C_{n}) = (C_{1} C_{2} \dots . C_{n - 1} C_{n}) (n + 1)^{n} / n!$

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Scarlett Discussed

C_{r} = .^{n} C_{r}

then prove that

(C_{0} + C_{1}) (C_{1} + C_{2}) \dots .. (C_{n - 1} + C_{n}) = (C_{1} C_{2} \dots . C_{n - 1} C_{n}) (n + 1)^{n} / n!

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C_{r} = .^{n} C_{r}

then prove that

(C_{0} + C_{1}) (C_{1} + C_{2}) \dots .. (C_{n - 1} + C_{n}) = (C_{1} C_{2} \dots . C_{n - 1} C_{n}) (n + 1)^{n} / n!