Step 1: Understanding the Concept:
Addition polymerisation joins monomers that contain double bonds, without loss of any small molecule. Condensation polymerisation joins bifunctional monomers with loss of water, ammonia or similar.
Step 2: Option (A):
The structure \([\text{CH}_2\text{-CH(CN)}]_n\) is polyacrylonitrile, made from acrylonitrile \(\text{CH}_2=\text{CH-CN}\) by addition polymerisation.
Step 3: Other options:
(B) \([\text{NH-(CH}_2)_5\text{-CO}]_n\) is nylon-6, made from caprolactam by ring-opening, a condensation type polyamide.
(C) The ester chain with \(\text{-O-CH}_2\text{CH}_2\text{-O-CO-C}_6\text{H}_4\text{-CO-}\) is terylene (PET), formed from ethylene glycol and terephthalic acid by condensation.
(D) The chain with \(\text{-O-CH(CH}_3)\text{-CH}_2\text{-CO-O-CH(C}_2\text{H}_5)\text{-CH}_2\text{-CO-}\) is PHBV, a polyester made by condensation of hydroxy acids.
Final Answer:
Only polyacrylonitrile is an addition polymer, option (A).
\[ \boxed{\text{Polyacrylonitrile}} \]