AMC 8 Daily Practice - Calculation Tricks by Grouping

This problem is somewhat unique and requires careful observation. We notice that the operation signs repeat every three numbers in the pattern .

Therefore, we can group every three numbers together. The sum of the first group is , the sum of the second group is , and the sum of the third group is , indicating that these sums form an arithmetic sequence with a common difference of .

Calculating the number of groups: terms, then groups with a remainder of term. Thus, there are complete groups.

We can rewrite the original expression as:

This forms an arithmetic sequence with: - First term - Common difference - Last term -

Applying the arithmetic series sum formula (Gauss's formula):

The final result is .