GATE 2017 CS (CS2) – Question 57

The ordinary generating function of {aₙ} is $(1+z)/(1-z)^3$. Find a₃−a₀.

Show answer and explanation

Correct answer: 15.0 to 15.0

Explanation

Use $(1-z)^{-3}=\sum_{n\ge0}\binom{n+2}{2}z^n$. Multiplying by 1+z gives a₀=1 and a₃= C(5,2)+C(4,2)=10+6=16. Hence a₃−a₀=15.

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