Part BCSIR NET June 2023generating-function

Generating function

Consider the function f defined by $f(z) = 1/(1 - z - z^{2})$ for $z \in \mathbb{C}$ such that $1 - z - z^{2} \ne 0$ . Which of the following statements is true?

A.f is an entire function.
B.f has a simple pole at z = 0.
C.f has a Taylor series expansion $f(z) = \sum a_{n}z^{n}$ , where $a_{0} = 1, a_{1} = 0$ and $a_{n}$ ₊ $_{2} = a_{n} + a_{n}$ ₊ $_{1}$ for n ≥ 0.
D.f has a Taylor series expansion $f(z) = \sum a_{n}z^{n}$ , where $a_{0} = 1, a_{1} = 1$ and $a_{n}$ ₊ $_{2} = a_{n} + a_{n}$ ₊ $_{1}$ for n ≥ 0.✓ Correct

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Generating function

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