2/1+6/1+12/1+...+110/1 21/2+77/2+165/2+...+1677/2+2021/2
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/06 03:31:49
2/1+6/1+12/1+...+110/1 21/2+77/2+165/2+...+1677/2+2021/2
2/1+6/1+12/1+...+110/1 21/2+77/2+165/2+...+1677/2+2021/2
2/1+6/1+12/1+...+110/1 21/2+77/2+165/2+...+1677/2+2021/2
题目应该是分子分母都倒过来写了.
(1)原式=1/1*2+1/2*3+1/3*4+.+1/10*11
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/10-1/11)
=1-1/11=10/11
(2)原式=2/3*7+2/7*11+……+2/39*43+2/43*47
=(1/2)*(1/3-1/7)+(1/2)*(1/7-1/11)+……+(1/2)*(1/39-1/43)+(1/2)*(1/43-1/47)
=(1/2)*(1/3-1/7+1/7-1/11+……+1/39-1/43+1/43-1/47)
=(1/2)*(1/3-1/47)
=(1/2)*44/141=22/141
2/1+6/1+12/1+...+110/1
=(1*2)/1+(2*3)/1+...+(10*11)/1
=1-2/1+2/1-3/1+...+10/1-11/1
=1-11/1
=11/10
21/2+77/2+165/2+...+1677/2+2021/2
=2*[(3*7)/1+(7*11)/1+...+(39*43)/1+(43*47)/1...
全部展开
2/1+6/1+12/1+...+110/1
=(1*2)/1+(2*3)/1+...+(10*11)/1
=1-2/1+2/1-3/1+...+10/1-11/1
=1-11/1
=11/10
21/2+77/2+165/2+...+1677/2+2021/2
=2*[(3*7)/1+(7*11)/1+...+(39*43)/1+(43*47)/1]
=2*[(3/1-7/1)*4/1+(7/1-11/1)*4/1+...+(43/1-47/1)*4/1]
=2*4/1*(3/1-7/1+7/1-11/1+...+43/1-47/1)
=2/1*(3/1-47/1)
=2/1*141/44
=141/22
希望对您有所帮助
如有问题，可以追问。
谢谢您的采纳
收起
2/1+6/1+12/1+...+110/1
=1-2/1+2/1-3/1+3/1-4/1+...+10/1-11/1
=1-11/1
=11/10
21/2+77/2+165/2+...+1677/2+2021/2
=2*(3*7/1+7*11/1+11*15/1+....+39*43/1+43*47/1)
=2*(4/1)*(3/1-7/1+7/1-11/1+11/1-15/1+.....+39/1-43/1+43/1-47/1)
=(2/1)*(3/1-47/1)
=(2/1)*(141/44)
=141/22