Final answer:
The underlined verb 'been' in the given sentence is in the past participle form, used to express a continuing state that began in the past.
Step-by-step explanation:
The form of the underlined verb in the sentence 'I've been tired since the beginning of the week' is d) past participle. The verb 'been' is a past participle used to form the present perfect continuous tense.
In this sentence, it is used with the auxiliary verb 'have' (contracted to 'I've'), which together indicate an action or state that began in the past and is continuing into the present.