Let (an), n = 1, 2, ... be a positive sequence of real numbers and it satisfies a₁ +2a2 + + nan = n(n+1)(n+2). (a) Find the values for a₁, a2, and a3. (b) Give a general expression for an. (c) Prove the expression you give satisfies (1) for all n € N+ by induction.

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