†extstyle∑_{r =0}^{n-1}(C(n,r))/(C(n,r)+C(n,r-1))

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n \sum r = 0 C (n, r)

C (n, r) + C (n, r - 1) = C (n + 1, r)

{(1 + x)}^{n} = n \sum r = 0^{n} C_{r}

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

C (n, r) + 2 C (n, r - 1) + C (n, r - 2)

{(1 + x)}^{n} = \sum_{r = 0}^{n} C_{r} x^{r}

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

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