8. (a) Give a combinatorial proof that n - (x + 1) = (*) + (=)...

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8. (a) Give a combinatorial proof that n - (x + 1) = (*) + ("=) k (b) Give a combinatorial proof that + + k (*) k k k.2 == +2 2 (c) Use Parts (a) and (b) to prove 12+22+ +n n(n + 1)(2n + 1) = 6 (This part does not need to be a combinatorial proof). 8. (a) Give a combinatorial proof that n - (x + 1) = (*) + ("=) k (b) Give a combinatorial proof that + + k (*) k k k.2 == +2 2 (c) Use Parts (a) and (b) to prove 12+22+ +n n(n + 1)(2n + 1) = 6 (This part does not need to be a combinatorial proof).