In the usual notation prove that C0 - C12 x - C23 x2 - - Cnn - 1 xn - 1 - xn - 1 - 1n - xx

If we take x from R.H.S to L.H.S the equations reduces to #160; C_0 x + C_1 #160; x^22 + C_2 x^33 + .... + C_nx^n + 1n + 1 = ...

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General Term of Binomial Expansion

In the usual ...

Question

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

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(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}

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

{(1 + x)}^{n}

c_{0} + \frac{c_{1}}{2} + \frac{c_{2}}{3} + . . . . . . + \frac{c_{n}}{n + 1} = \frac{2^{n + 1} - 1}{n + 1}

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

(1 + x)^{n}

c_{0} + \frac{c_{1}}{2} + \frac{c_{2}}{3} + . . . . . + \frac{c_{n}}{n + 1} = \frac{2^{n + 1} - 1}{n + 1}

c_{0}, c_{1}, c_{2}

(1 + x)^{n}

c_{1} + c_{1} c_{2} + c_{2} c_{3} + . . . . . . . c_{n - 1} c_{n} = \frac{(2 n)!}{(n + 1)! (n - 1)!}

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