1²-2²+3²-4²+5-6²+.-100²+101²

来源：学生作业帮助网编辑：作业帮时间：2024/05/06 03:11:21

1²-2²+3²-4²+5²-6²+…-100²+101²
=1²+(3²-2²)+(5²-4²)+(7²-6²)+...+(101²-100²)
=1+(3+2)(3-2)+(5+4)(5-4)+(7+6)(7-6)+...+(101+100)(101-100)
=1+2+3+4+5+6+7+...+100+101
=101×102÷2
=5151

1²-2²+3²-4²+5-6²+.....-100²+101²
=1+(3²-2²)+(5²-4²)+...+(101²-100²)
=1+(3-2)*(3+2)+...+(101-100)*(101+100)
=1+2+3+...+100+101
=5151