二乘四分之一加四乘六分之一加上六乘八分之一加...加二零零六乘二零零八分之一是多少?1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2006*2008)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 00:02:17
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二乘四分之一加四乘六分之一加上六乘八分之一加...加二零零六乘二零零八分之一是多少?1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2006*2008)
二乘四分之一加四乘六分之一加上六乘八分之一加...加二零零六乘二零零八分之一是多少?
1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2006*2008)
二乘四分之一加四乘六分之一加上六乘八分之一加...加二零零六乘二零零八分之一是多少?1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2006*2008)
因为1/(2×4)=1/2×(1/2-1/4)
1/(4×6)=1/2×(1/4-1/6)
所以1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2006*2008)
=1/2×(1/2-1/4+1/4-1/6+……+1/2006-1/2008)
=1/2×(1/2-1/2008)
=1/2×1003/2008
=1003/4016
1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2006*2008)
=1/4*(1/1*2+1/2*3+1/3*4+...+1/1003*1004)
=1/4*(1-1/2+1/2-1/3+1/3-1/4+...+1/1003-1/1004)
=1/4*1003/1004
=1003/4016
1/(2*4)+1/(4*6)+1/(6*8)+……+1/(2006*2008)
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+......+1/2*(1/2006-1/2008)
=1/2*(1/2-1/4+1/4-1/6+1/8-1/8+......+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*1003/2008
=1003/4016