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5 5 (a) Evaluate: (i) (k – 1)(k+1) (ii) II (471) ) П k+ k=0 k=0 (b) The Catalan numbers' Cn, which have several applicat
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5 5 (a) Evaluate: (i) (k – 1)(k+1) (ii) II (471) ) П k+ k=0 k=0 (b) The Catalan numbers' Cn, which have several applicat
5 5 (a) Evaluate: (i) (k – 1)(k+1) (ii) II (471) ) П k+ k=0 k=0 (b) The Catalan numbers' Cn, which have several applications in computing, may be defined implicitly by Co = 1 and Cn+1 = <-, C;Cn-j. Evaluate Cs. See https://en.wikipedia.org/wiki/Catalan_number for many interesting prop- erties of Catalan numbers, and of Cs in particular.
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