Final answer:
The sum of integers in the 500th group that Ed typed is 31972, which is found by calculating the sum of integers from 3993 to 4000, leading to an average of 3996.5 multiplied by 8. However, this sum does not match the options provided in the problem, suggesting a possible error in the question or options.
Step-by-step explanation:
To find the sum of the integers in the 500th group that Ed typed, we need to first determine which integers are in this group. Since Ed typed the integers in groups of 8, we can determine the first and last integer in the 500th group by considering the pattern:
- The first group contains integers 1 to 8, so the sum is 1+2+3+4+5+6+7+8.
- The second group contains integers 9 to 16, and so on.
Therefore, the 500th group will start with the integer (500-1)×8 + 1 = 3993 and end with the integer 500×8 = 4000. The sum of the integers from 3993 to 4000 is:
- 3993 + 3994 + 3995 + 3996 + 3997 + 3998 + 3999 + 4000
The sum of these consecutive integers is calculated by taking the average of the first and last integer and multiplying by the number of integers. Thus we have:
(3993 + 4000) / 2 × 8 = 7993 / 2 × 8 = 3996.5 × 8 = 31972.
This result does not match any of the options provided in the question, possibly due to an error in either the question itself or in the provided options. Based on the correct calculation, the sum of the integers in the 500th group typed by Ed is 31972.