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The word 感激不尽 is formed by combining the compound 感激, meaning "gratitude" (感 contributing "feeling" and 激 "arouse"), with the phrase 不尽, meaning "endless" (不 as a negator and 尽 meaning "to exhaust"). The structure places 不尽 after 感激 to act as a modifier, literally conveying "gratitude that is not exhausted" to express intense thankfulness.

Word Definition - 感激不尽

gǎn jī bù jìn can't thank sb enough (idiom)