1/1×3+1/2×4+…1/2008×2010+1/2009×2011的结果

来源：学生作业帮助网 编辑：作业帮 时间：2024/12/02 18:56:58
1/1×3+1/2×4+…1/2008×2010+1/2009×2011的结果
xTJ@.t榓BHH-PD E6}f/fBX 7ɽs&w.159eXެ;F9Y/4wpfcL.9EPX H܀(dU$A 9nWw]-E+JXFB2*J!3*DAt˨ WKnȌ ]gֆ_ˮ@qg lxhC:YOY?ywscIg3f|B,O[֡xn")GÙO9=:"6۹v]+jtΐWS{: "9clbyA>ύ4

1/1×3+1/2×4+…1/2008×2010+1/2009×2011的结果
1/1×3+1/2×4+…1/2008×2010+1/2009×2011的结果

1/1×3+1/2×4+…1/2008×2010+1/2009×2011的结果
1/1×3+1/2×4+…1/2008×2010+1/2009×2011
=(1/2)×(1-1/3)+(1/2)×(1/2-1/4)+.+(1/2)(1/2008-1/2010)+(1/2)(1/2009-1/2011)
=(1/2)(1-1/3+1/3-1/5+1/5-.-1/2009+1/2009-1/2011)+(1/2)(1/2-1/4+.-1/2008
+1/2008- 1/2010)
=(1/2)×(1-1/2011)+(1/2)×(1/2-1/2010)
=(1/2)×(1+1/2-1/2011-1/2010)
=(1/2)×(6059144/4042110)
=1514786/2021055

1/1×3+1/2×4+…1/2008×2010+1/2009×2011
=(1/2)×(1-1/3)+(1/2)×(1/2-1/4)+............+(1/2)(1/2008-1/2010)+(1/2)(1/2009-1/2011)
=(1/2)(1-1/3+1/3-1/5+1/5-.......-1/2009+1/2009-1/2011)+(1/2)(...

全部展开

1/1×3+1/2×4+…1/2008×2010+1/2009×2011
=(1/2)×(1-1/3)+(1/2)×(1/2-1/4)+............+(1/2)(1/2008-1/2010)+(1/2)(1/2009-1/2011)
=(1/2)(1-1/3+1/3-1/5+1/5-.......-1/2009+1/2009-1/2011)+(1/2)(1/2-1/4+.......-1/2008+1/2008-1/2010)
=(1/2)×(1-1/2011)+(1/2)×(1/2-1/2010)
=(1/2)×(1+1/2-1/2011-1/2010)
=(1/2)×(6059144/4042110)
=1514786/2021055
脚都打酸了。。。这么多。。为了练习打字。。照楼上的再打一遍。。花了我半个小时。。郁闷。。这么多。。

收起

(1-1/2)×(1-1/3)×(1-1/4)……×（1-1/2008）计算方法 1/2008+2/2008+3/2008+4/2008……+2007/2008（简算） | 1/3 - 1/2 | + | 1/4 - 1/3 | + | 1/5 - 1/4 | …… + | 1/2009 - 1/2008| |1-1/2|+|1/2-1/3|+|1/3-1/4|+……|1/2007-1/2008|=? |1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2009-1/2008| 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + ……+ 1/2008*2009 简便计算,(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)/(1/1005+1/1006+1/1007+…1/2007+1/2008) 计算：(3+1)(3^2+1)(3^4+1)…(3^2008+1)-3^4016/2 （1-1/2+1/3-1/4+1/5-…+1/2007-1/2008）除以（1/1005+1/1006+…1/2007+1/2008）=?急 (1-1/2²)(1-1/3²)(1-1/4²)……*(1-1/2008²) 【在线等待】1/2+(1/4+3/4)+(1/6+3/6+5/6)+……+(1/2008+3/2008+5/2008…+2007/2008) 还要说明 2008-2008*1/2-{2008-2008*1/2}*1/3-{2008-2008*1/2-{2008-2008*1/2}*1/3}1/4-.-余的1/2008= (-1)+(+2)+(-3)+(+4)+……+(-2005)+(+2006)+(-2007)+(+2008) 1+2+3+4……+2008+2009+2010=? 1-1/2 +1/2-1/3+1/3-1/4+…1/2008-1/2009的计算方法 （-1×1/2）+（-1/2×1/3）+（-1/3×1/4）+…+（-1/2008×1/2009） 找规律计算:(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2007×1/2008) 计算1×1!+2×2!+3×3!+4×4!+…2008×2008!+2009×2009!