If (1 + x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + ... + C_n x^n , then prove that ΣΣ_(0≤i<j≤n) ((i/(^n C_i )) + (j/(^n C_j ))) = (n^2 /2)(Σ_(r=0) ^n (1/(^n C


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Question Number 23250 by Tinkutara last updated on 28/Oct/17

$I f {(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + C_{3} x^{3}$ $+ . . . + C_{n} x^{n}, t h e n p r o v e t h a t$ $\underset{0 ⩽ i < j ⩽ n}{Σ Σ} (\frac{i}{^{n} C_{i}} + \frac{j}{^{n} C_{j}}) = \frac{n^{2}}{2} (\underset{r = 0}{\sum^{n}} \frac{1}{^{n} C_{r}}) .$
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