1+3=4=2² 1+2+5=9=3² 1+3+5+7=16=4² 1+3+5+7+9=25=5²(1)请猜想1+3+5+7+9+……+19=____(2)请猜想1+3+5+7+9+……+(2n-1)+(2n+1)+(2n+3)=____(3)请用上述规律计算:103+105+107+……+2003+2005
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 11:33:49
![1+3=4=2² 1+2+5=9=3² 1+3+5+7=16=4² 1+3+5+7+9=25=5²(1)请猜想1+3+5+7+9+……+19=____(2)请猜想1+3+5+7+9+……+(2n-1)+(2n+1)+(2n+3)=____(3)请用上述规律计算:103+105+107+……+2003+2005](/uploads/image/z/673448-32-8.jpg?t=1%2B3%3D4%3D2%26%23178%3B+1%2B2%2B5%3D9%3D3%26%23178%3B+1%2B3%2B5%2B7%3D16%3D4%26%23178%3B+1%2B3%2B5%2B7%2B9%3D25%3D5%26%23178%3B%EF%BC%881%EF%BC%89%E8%AF%B7%E7%8C%9C%E6%83%B31%2B3%2B5%2B7%2B9%2B%E2%80%A6%E2%80%A6%2B19%3D____%EF%BC%882%EF%BC%89%E8%AF%B7%E7%8C%9C%E6%83%B31%2B3%2B5%2B7%2B9%2B%E2%80%A6%E2%80%A6%2B%282n-1%29%2B%282n%2B1%29%2B%282n%2B3%29%3D____%EF%BC%883%EF%BC%89%E8%AF%B7%E7%94%A8%E4%B8%8A%E8%BF%B0%E8%A7%84%E5%BE%8B%E8%AE%A1%E7%AE%97%EF%BC%9A103%2B105%2B107%2B%E2%80%A6%E2%80%A6%2B2003%2B2005)
1+3=4=2² 1+2+5=9=3² 1+3+5+7=16=4² 1+3+5+7+9=25=5²(1)请猜想1+3+5+7+9+……+19=____(2)请猜想1+3+5+7+9+……+(2n-1)+(2n+1)+(2n+3)=____(3)请用上述规律计算:103+105+107+……+2003+2005
1+3=4=2² 1+2+5=9=3² 1+3+5+7=16=4² 1+3+5+7+9=25=5²
(1)请猜想1+3+5+7+9+……+19=____
(2)请猜想1+3+5+7+9+……+(2n-1)+(2n+1)+(2n+3)=____
(3)请用上述规律计算:
103+105+107+……+2003+2005
1+3=4=2² 1+2+5=9=3² 1+3+5+7=16=4² 1+3+5+7+9=25=5²(1)请猜想1+3+5+7+9+……+19=____(2)请猜想1+3+5+7+9+……+(2n-1)+(2n+1)+(2n+3)=____(3)请用上述规律计算:103+105+107+……+2003+2005
可以总结出规律:结果就等于第一个和最后一个和的一半的平方.
1)1+3+5+7+9+……+19,1+19=20,所以结果等于10的平方:1002
2)1+2n+3=2n+4,它的一半是n+2,所以结果等于它的平方:n²+4n+4
3) 1+2+3+...+2005 的结果是1003的平方:1006009
1+2+3+.+101 的结果是51的平方:2601
所以计算结果为:1006009-2601 = 1003408