Calculate the first six terms of each of the following sequences {a_n} and draw a graph of a_n against 1.
(Some care is needed in choosing the scale of the y axis.) What is the behaviour of a_n as n → ∞?

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(a) an = (b) a = 'n n n + 1 3n + 2n + 1 6n + 5n+ 2 1+ (c) a, (2n) (n 1) (d) an (e) a = (1 + a_1), a = 1 (n=2) 2 (n 1) 1 2n (n 1) n - (f) a, = = sin n 2 n (n=1) n (n 1)