(2.1) Determine a generating function for the finite sequence n {(). (1) ·····(²₁). ()}. (2.2) Consider the sequence (ak
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(2.1) Determine a generating function for the finite sequence n {(). (1) ·····(²₁). ()}. (2.2) Consider the sequence (ak) =(4,9, 19, 39, 79, ... ). (2.2.1) Define the sequence (ak) recursively. (2.2.2) Show that a generating function G(r) for (ak) is given by G(r) = (2.2.3) Given that G(r) can be expanded as G(r) derive a general formula for a. 4 - 3x (1-x)(1-2x)* 5 1-2x 1 1- x'