1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+…+1/18*20+1/38
来源:百度知道 编辑:UC知道 时间:2024/07/07 08:12:41
可以这么解题:
1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+…+1/18*20+1/38
=1/2 *(1-1/3 + 1/2-1/4 + 1/3+1/5 + 1/4-1/6....+1/17-1/19 + 1/18-1/20) + 1/38
=1/2 * (1+1/2-1/19-1/20) + 1/38
=3/4-39/760+1/38
=3/4-19/760
通式1/1*3+1/2*4+1/3*5+....+1/n(n+2)
=1/2(1/1-1/3)+1/2(1/2-1/4)+1/2(1/3-1/5)+1/2[1/n-1/(n+2)]
=1/2[1-1/3+1/2-1/4+1/3-1/5+....+1/n-1/(n+2)]
=1/2[1+1/2-1/n-1/(n+2)]
所以 原式=1/2[1+1/2-1/18-1/20]+1/38
=251/180+1/38
最后结果很难算!!!!!!!!!!!!!!!!!!!
1/(2n-1)(2n+1)=1/2(1/2n-1 -1/2n+1)
1/2(1-1/20)+1/38=19/40+1/38=381/760
(1+1/2+1/3+1/4)×
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+1/2+1/3+1/4+......1/2002=?
1-1/2+1/3-1/4+........1/99-1/100
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
1/1*2+1/2*3+1/3*4+...+1/99*100
1/1*2+1/2*3+1/3*4+..........+1/2002*2003
1*(1/2)+2*(1/3)+3*(1/4)+...+99*(1/100)
1/1*2+1/2*3+1/3*4+......+1/9*10