请先阅读下列一组内容,
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/11/12 19:23:16
请先阅读下列一组内容,
∵1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,.,1/9*10=1/9-1/10,
∴1/1*2+1/2*3+1/3*4+.+1/9*10=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/9-1/10)=1-1/2+1/2-1/3+1/3-1/4+.+1/9-1/10=1-1/10=9/10.
计算:(1)1/1*2+1/2*3+1/3*4+.+1/2004*2005;
(2)1*/1*3+1/3*5+1/5*7+.+1/49*51.
∵1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,.,1/9*10=1/9-1/10,
∴1/1*2+1/2*3+1/3*4+.+1/9*10=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/9-1/10)=1-1/2+1/2-1/3+1/3-1/4+.+1/9-1/10=1-1/10=9/10.
计算:(1)1/1*2+1/2*3+1/3*4+.+1/2004*2005;
(2)1*/1*3+1/3*5+1/5*7+.+1/49*51.
(2)1/1*2+1/2*3+1/3*4+.+1/2004*2005
=1-1/2+1/2-1/3+1/3-1/4+……+1/2004-1/2005
=1- 1/2005
=2004/2005
(3)1*/1*3+1/3*5+1/5*7+.+1/49*51.
= 1/2*( 1-1/3+1/3-1/5+1/5-1/7……+1/49-1/51)
=1/2* 50/51
=25/ 51
请采纳...
再问: 你也回答的详细点行么
再答: 裂项相消
1/1*2+1/2*3+1/3*4+......+1/2004*2005
=1-1/2+1/2-1/3+1/3-1/4+……+1/2004-1/2005
这里-1/2+1/2抵消, -1/3+1/3抵消……
=1- 1/2005
=2004/2005
再问: 我怎么感觉你第2题写错了???
再答: 改了,之前激动了,1-1/51应该 = 50/51
1*/1*3+1/3*5+1/5*7+......+1/49*51.
= 1/2*( 1-1/3+1/3-1/5+1/5-1/7……+1/49-1/51)
=1/2* 50/51
=25/ 51
=1-1/2+1/2-1/3+1/3-1/4+……+1/2004-1/2005
=1- 1/2005
=2004/2005
(3)1*/1*3+1/3*5+1/5*7+.+1/49*51.
= 1/2*( 1-1/3+1/3-1/5+1/5-1/7……+1/49-1/51)
=1/2* 50/51
=25/ 51
请采纳...
再问: 你也回答的详细点行么
再答: 裂项相消
1/1*2+1/2*3+1/3*4+......+1/2004*2005
=1-1/2+1/2-1/3+1/3-1/4+……+1/2004-1/2005
这里-1/2+1/2抵消, -1/3+1/3抵消……
=1- 1/2005
=2004/2005
再问: 我怎么感觉你第2题写错了???
再答: 改了,之前激动了,1-1/51应该 = 50/51
1*/1*3+1/3*5+1/5*7+......+1/49*51.
= 1/2*( 1-1/3+1/3-1/5+1/5-1/7……+1/49-1/51)
=1/2* 50/51
=25/ 51