问题
填空题
计算(22+42+62+82+…+1002)-(12+32+52+72+…+992)=______.
答案
(22+42+62+82+…+1002)-(12+32+52+72+…+992),
=(22-12)+(42-32)+(62-55)+(82-72)+…+(1002-992),
=(2+1)×(2-1)+(4+3)×(4-3)+(6+5)×(6-5)+(8+7)×(8-7)+…+(100+99)×(100-9),
=3+7+11+15+…+199,
=(3+199)×[(199-3)÷4+1]÷2,
=202×50÷2,
=5050.
故答案为:5050.