If ` (1 + x)^(n) = sum_(r=0)^(n) C_(r),x^(r)`, then prove that
`(sumsum)_(0leiltjlen) ((i)/(C_(i)) + (j)/(C_(j))) = (n^(2))/(2) sum_(r=0)^(n) (1)/(C_(r))` .

Explanation

To prove the given statement, we will follow a systematic approach. Let's denote the expression we want to prove as \( S \):

\[ S = \sum_{0 \leq i < j \leq n} \left( \frac{1}{C_i} + \frac{1}{C_j} \right) \]

where \( C_r = \binom{n}{r} \).

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