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请先阅读下列一组内容,1/1x2+1/2x3+1/3x4...+1/9x10=（1-1/2）+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)=1+1/2-1/3+1/3+1/4+...+1/9-1/10=9/10计算：①1/1x2+1/2x3+1/3x4+...+1/2004x2005=②1/1x3+1/3x5+1/5x7+...+1/49x51=
题目详情
请先阅读下列一组内容,
1/1x2+1/2x3+1/3x4...+1/9x10=（1-1/2）+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)=1+1/2-1/3+1/3+1/4+...+1/9-1/10=9/10
计算：①1/1x2+1/2x3+1/3x4+...+1/2004x2005=
②1/1x3+1/3x5+1/5x7+...+1/49x51=
1/1x2+1/2x3+1/3x4...+1/9x10=（1-1/2）+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)=1+1/2-1/3+1/3+1/4+...+1/9-1/10=9/10
计算：①1/1x2+1/2x3+1/3x4+...+1/2004x2005=
②1/1x3+1/3x5+1/5x7+...+1/49x51=
▼优质解答
答案和解析
：①1/1x2+1/2x3+1/3x4+...+1/2004x2005
=1-1/2+1/2-1/3+……+1/2004-1/2005
=1-1/2005
=2004/2005
②1/1x3+1/3x5+1/5x7+...+1/49x51
=1/2×（1-1/3+1/3-1/5+……+1/49-1/51）
=1/2×（1-1/51）
=1/2×50/51
=25/51
=1-1/2+1/2-1/3+……+1/2004-1/2005
=1-1/2005
=2004/2005
②1/1x3+1/3x5+1/5x7+...+1/49x51
=1/2×（1-1/3+1/3-1/5+……+1/49-1/51）
=1/2×（1-1/51）
=1/2×50/51
=25/51
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