使用 (a + b)(a - b) = a² - b²
2001² - 2000² + 1999² - 1998² + ...+ 3² - 2² + 1²
= (2001² - 2000²) + (1999² - 1998²) + ...+ (3² - 2²) + 1²
= (2001 + 2000)(2001 - 2000) + (1999 + 1998)(1999 - 1998) + ...+ (3 + 2)(3 - 2) + 1
= (2001 + 2000) * 1 + (1999 + 1998) * 1 + ...+ (3 + 2) * 1 + 1
= 2001 + 2000 + 1999 + 1998 + .+ 3 + 2 + 1
= (1 + 2001) * 2001 / 2 (梯形公式)
= 2003001为什么（a+b）（a-b）=a²-b²？公式呀！
(a + b) (a - b) = a(a + b) - b(a + b) = a² + ab - ab - b² = a² - b²