mwbr.net
当前位置:首页 >> 1+1/2+1/3+......+1/2002)*(1/2+1/3+1/4+......+1/... >>

1+1/2+1/3+......+1/2002)*(1/2+1/3+1/4+......+1/...

=[(1/2+1/3+......+1/2002)*(1/2+1/3+1/4+......+1/2003) +(1/2+1/3+1/4+......+1/2003)] -[(1/2+1/3+1/4+......+1/2002)*(1/2+1/3+......+1/2003)+(1/2+1/3+1/4+......+1/2002)] =(1/2+1/3+1/4+......+1/2003) -(1/2+1/3+1/4+......+1/2002) =1...

1/1*2+1/2*3+1/3*4+......1/2001*2002+1/2002*2003 =1-1/2+1/2-1/3+1/3-1/4+……+1/2001-1/2002+1/2002-1/2003 =1-1/2003 =2002/2003

解 令a=1/2+1/3+......+1/2002,则原式变为 (a+1/2003)*(1+a)-(1+a+1/2003)*a =a+a ²+1/2003+1/2003a-(a+a ²+1/2003a) =1/2003 数学辅导团为您解答,不理解请追问

1/2+1/3+1/4+1/5+1/6+......+1/2001+1/2002+1/2003=7.17986660535804

1/n(n+1) = 1/n - 1/(n+1) 1/1×2+1/2×3+1/3×4...+1/2002×2003 = (1/1 - 1/2) +(1/2 - 1/3) + (1/3 - 1/4) +... + (1/2002 -1/2003 ) = 1 - 1/2003 = 2002/2003

题没完。。。

设:1/2+1/3+1/4+...+1/2002=a 1/2+1/3+1/4+...+1/2002+1/2003=b 原式=(1+a)b-a(1+b) =b+ab-a-ab =a-b =1/2003

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+..+(1/2001-1/2002) =1-1/2002=2001/2002

1+2+3+4......+2001+2002+2003+2002+2001...+3+2+1 =2002*(1+2002)/2+2003+2002*(1+2002)/2 =2002*2003+2003 =2003*2003 =4012009

原式=1+1/3+...+1/【(1+2002)x2002÷2】 =2/2+2/6+...2/(2002x2003) =2x(1-1/2+1/2-1/3+....1/2002-1/2003) =2x(1-1/2003) =2x2002/2003 =4004/2003

网站首页 | 网站地图
All rights reserved Powered by www.mwbr.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com