答好加150分1-1/2+1/3-1/4+.+1/99-1/100--------------------------------------------------------------------1/(1+101)+1/(2+102)+1/(3+103)+1/(4+104)+.+1/(49+149)+1/(50+150)
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/25 03:28:32
![答好加150分1-1/2+1/3-1/4+.+1/99-1/100--------------------------------------------------------------------1/(1+101)+1/(2+102)+1/(3+103)+1/(4+104)+.+1/(49+149)+1/(50+150)](/uploads/image/z/2654752-40-2.jpg?t=%E7%AD%94%E5%A5%BD%E5%8A%A0150%E5%88%861-1%2F2%2B1%2F3-1%2F4%2B.%2B1%2F99-1%2F100--------------------------------------------------------------------1%2F%281%2B101%29%2B1%2F%282%2B102%29%2B1%2F%283%2B103%29%2B1%2F%284%2B104%29%2B.%2B1%2F%2849%2B149%29%2B1%2F%2850%2B150%29)
答好加150分1-1/2+1/3-1/4+.+1/99-1/100--------------------------------------------------------------------1/(1+101)+1/(2+102)+1/(3+103)+1/(4+104)+.+1/(49+149)+1/(50+150)
答好加150分
1-1/2+1/3-1/4+.+1/99-1/100
--------------------------------------------------------------------
1/(1+101)+1/(2+102)+1/(3+103)+1/(4+104)+.+1/(49+149)+1/(50+150)
答好加150分1-1/2+1/3-1/4+.+1/99-1/100--------------------------------------------------------------------1/(1+101)+1/(2+102)+1/(3+103)+1/(4+104)+.+1/(49+149)+1/(50+150)
分子
=1-1/2+1/3-1/4+.+1/99-1/100
=1+1/3+.+1/99-(1/2+1/4+.+1/100)
=1+1/3+.+1/99+(1/2+1/4+.+1/100)-2*(1/2+1/4+.+1/100)
=1+1/2+1/3+1/4+.+1/99+1/100-(1+1/2+1/3+.+1/50)
令sn=1+1/2+1/3+……+1/n
所以分子=s100-s50
分母
=1/(1+101)+1/(2+102)+1/(3+103)+.+1/(n+100+n)+.+1/(50+150)
=1/(2+100)+1/(4+100)+1/(6+100)+.+1/(2n+100)+.+1/(2*50+100)
=[1/(1+50)+1/(2+50)+.+1/(n+50)+.+1/(50+50)]/2
=(1/51+1/52+.+1/100)/2
=(s100-s50)/2
所以
分子/分母=(s100-s50)/[(s100-s50)/2]=2