请问(2/2009+4/2009+6/2009+···+2008/2009)—(1/2009+3/2009+5/2009+···+2007/2009)等于多少?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/24 06:53:24
请问(2/2009+4/2009+6/2009+···+2008/2009)—(1/2009+3/2009+5/2009+···+2007/2009)等于多少?
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请问(2/2009+4/2009+6/2009+···+2008/2009)—(1/2009+3/2009+5/2009+···+2007/2009)等于多少?
请问(2/2009+4/2009+6/2009+···+2008/2009)—(1/2009+3/2009+5/2009+···+2007/2009)等于多少?

请问(2/2009+4/2009+6/2009+···+2008/2009)—(1/2009+3/2009+5/2009+···+2007/2009)等于多少?
(2/2009+4/2009+6/2009+···+2008/2009)—(1/2009+3/2009+5/2009+···+2007/2009)
=[(2+4+6+...+2008)-(1+3+5+...+2007)]/2009
=[(2-1)+(4-3)+(6-5)+...+(2008-2007)]/2009
=1004/2009

简便解法:打开两个括号后变为2/2009+4/2009+…... -1/2009-3/2009-......
由上可知:2/2009-1/2009=1/2009,4/2009-3/2009=1/2009。 那么共有(2008/2)个1/2009,结果就是1004*1/2009=1004/2009