Evaluate the sum $$1 + 2 + 3 - 4 - 5 + 6 + 7 + 8 - 9 - 1 0 + . . . - 2010$$, where each three consecutive signs $+$ are followed by two signs $-$.
Source: 2010 Saudi Arabia BMO TST 5.2 - Balkan Math Olympiad
Tags: algebra, Sum
Evaluate the sum $$1 + 2 + 3 - 4 - 5 + 6 + 7 + 8 - 9 - 1 0 + . . . - 2010$$, where each three consecutive signs $+$ are followed by two signs $-$.