Question: 2n +3 n+1 (a) Derive an expression for n(n+1)3 2n +1 1 (b) Show that, for all N21, = (n +1)(n + 2n +2)

2n +3 n+1 (a) Derive an expression for n(n+1)3 2n +1 1

2n +3 n+1 (a) Derive an expression for n(n+1)3 2n +1 1 (b) Show that, for all N21, = (n +1)(n + 2n +2) 2 (c) (i) By considering (2r + 1) -(2r - 1)', derive an expression for r. (ii) Prove by mathematical induction that (3r* +r')=n'(n+1)', for all n21. (ii) Use the results from (i) and (ii) to derive a simplified expression for 2r

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