4. Consider the following identity: n 2 2n Σ (3) - (30) n (1) Perhaps it seems mysterious? But if you try a few small values of n, you may begin to suspect it is correct. (a) Suppose n N and that we have a set S of cardinality 2n containing n distinct objects, all coloured red, and n distinct objects, all coloured blue. Let ke Z satisfy 0 ≤ k

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