Final answer:
In Erikson's stage of late adulthood, the successful completion of the developmental task allows the elderly to feel a sense of integrity, reflecting on life with few regrets, and prepares them for the end of life with a sense of fulfilment.
Step-by-step explanation:
When planning a health program for elderly adults that integrates Erik Erikson's theory of task development, the nurse recognizes that the stage of late adulthood is characterized by the developmental task of integrity versus despair. In this stage, successful completion of the task allows the person to reflect on their life and feel a sense of integrity, looking back with few regrets. On the contrary, those unable to achieve this may experience feelings of bitterness and despair.
Erikson's theory proposes that we go through eight developmental stages over our lifespan, with each stage presenting a challenge, or task, that we need to master. The successful navigation of these challenges leads to a sense of competence and a healthy personality. Particularly in late adulthood, mastering the challenge of integrity versus despair can open up potential for creativity, new activities, and peaceful preparation for life's end.