Why is the coefficient $21/8$?
2026-04-13 17:39:11.1776101951
How to find the coefficient of taylor series
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The only way you can get "$x^2$" multiplying those two sums is $(1)(z^2/4)$, $(1)(4z^2)$ (you have "4z" but, since you already have "2z", assume "$4z^2$" was what you intended), and $(2z)(z/2)$ so you have $z^2/4+ 4z^2+ z^2= (1/4+ 5)Z^2= 21/4$. Since the entire expression is multiplied by $1/2$, you get $21/8$.