1/1*4+1/4*7+1/7*10......+1/2002*2005(简算)
来源:百度知道 编辑:UC知道 时间:2024/05/09 03:20:02
1/1×4+1/4×7+1/7×10+...+1/2002×2005
=(1/3)×(1/1-1/4)+(1/3)×(1/4-1/7)+(1/3)×(1/7-1/10)+...+(1/3)×(1/2002-1/2005)
=(1/3)×(1/1-1/4+1/4-1/7+1/7-1/10+...+1/2002-1/2005)
=(1/3)×(1-1/2005)
=(1/3)×(2004/2005)
=668/2005
原式=1*2002+(3/1+3/4+3/7+…3/2002)
=2002+3(1/1+1/4+1/7+…1/2002)
=2002+3*[1/3(3-1+1-1/4+1/4-1/7+…+1/1999-1/2002)
=2002+2又2001/2002
=2004又2001/2002
呵呵,加油!有什么不懂的再问,诚答!
1/(n*(n+3))=(1/n-1/(n+3))/3
原式=(1-1/4+1/4-1/7+...+1/2002-1/2005)/3
=(2004/2005)/3
=668/2005
(1+1/2+1/3+1/4)×
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
(1-1/4)(1-1/9)(1-1/16)^(1-1/4008004)(1-1/4012009)
1+1/2+1+1/3+1+1/4+......+1/100=?
1/1+1/2+1/3+1/4+。。。。+1/N 是多少
1-1/4 -1/8-1/16-1/32-1/64
1/1+1/2+1/3+1/4+......1/2002=?
1-1/2+1/3-1/4+........1/99-1/100
s=1/1+1/1!+1/2!+1/3!+1/4!+....+1/25!
1/2+1/4+1/8+1/16......+1/256=?