In the usual notations prove that C0 - C1C1 - C2-Cn - 1 - Cn - n - 1nn-C1C2C3-Cn

We have prove that #160; (C_0 + C_1)C_1 (C_1 + C_2)C_2 ......C_n 1 + C_nC_n = (n + 1)^nn! or #160; ( C_0C_1 + 1 ) ( C_1C_2 + ...

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Triangle Law for Vector Addition

In the usual ...

Question

In the usual notations prove that
$(C_{0} + C_{1}) (C_{1} + C_{2}) . . . . . (C_{n - 1} + C_{n})$
$= \frac{(n + 1)^{n}}{n!} C_{1} C_{2} C_{3} . . . . . C_{n}$

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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_{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 - -}

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

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

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