Question

1²-2²+3²-4²+......+99²-10²=101² 计算

1²-2²+3²-4²+......+99²-100²+101² 计算

Answer 1

1²-2²+3²-4²+......+99²-100²+101²
=101²-100²+...+3²-2²+1²
=（101+100）（101-100）+（99+98）（99-98）+...+（3+2）（3-2）+1
=201+197+...+5+1
=（201+1）×51÷2
=5151

Answer 2

1²-2²+3²-4²+......+99²-100²+101²
=(1+2)(1-2)+(3+4)(3-4)+....+(99+100)(99-100)+101²
=-(1+2+3+4+.....+99+100)+101²
= -100*(100+1)/2+101²
= 101*(101-50)
= 101*51
=5151

Answer 3

平方差
=(101+100)(101-100)+……+(2+1)(2-1)
=(101+100)×1+……+(2+1)×1
=101+100+……+2+1
=5151