$\frac{(C_{0} + C_{1}) (C_{1} + C_{2}) (C_{2} + C_{3}) . . . . . (C_{n - 1} + C_{n})}{C_{0} + C_{1} (C_{2} . . . . . . C_{n})} =$

\frac{{(n + 1)}^{n}}{n!}

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\frac{{(n + 2)}^{n}}{n!}

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\frac{{(n + 1)}^{n - 1}}{n!}

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\frac{{(n - 1)}^{n}}{n!}

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(C_{0} + C_{1}) (C_{1} + C_{2}) (C_{2} + C_{3}) (C_{3} + C_{4}) . . . . . (C_{n - 1} + C_{n}) = \frac{C_{0} C_{1} C_{2} . . . . C_{n - 1} {(n + 1)}^{n}}{n!}

(C_{0} + C_{1}) (C_{1} + C_{2}) . . . . . (C_{n - 1} + C_{n})

= \frac{(n + 1)^{n}}{n!} C_{1} C_{2} C_{3} . . . . . C_{n}

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n}

(C_{0} + C_{1}) (C_{1} + C_{2}) \dots (C_{n - 1} + C_{n}) = k \cdot C_{1} C_{2} C_{3} \dots C_{n}

k

c_{0}, c_{1}, c_{2}, . . . . . . . c_{n}

{(1 + x)}^{n}

(c_{0} + c_{1}) (c_{1} + c_{2}) . . . . . . . (c_{n - 1} + c_{n}) = \frac{c_{1} c_{2} . . . c_{n} {(n + 1)}^{n}}{| n - -}

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

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(C0+C1)(C1+C2)(C2+C3).....(Cn−1+Cn)C0+C1(C2......Cn)=