1/2+1/3+2/3+1/4+2/4+3/4+1/5+……+1/60+2/60+……+59/60
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 19:01:15
![1/2+1/3+2/3+1/4+2/4+3/4+1/5+……+1/60+2/60+……+59/60](/uploads/image/z/3141680-32-0.jpg?t=1%2F2%2B1%2F3%2B2%2F3%2B1%2F4%2B2%2F4%2B3%2F4%2B1%2F5%2B%E2%80%A6%E2%80%A6%2B1%2F60%2B2%2F60%2B%E2%80%A6%E2%80%A6%2B59%2F60)
1/2+1/3+2/3+1/4+2/4+3/4+1/5+……+1/60+2/60+……+59/60
1/2+1/3+2/3+1/4+2/4+3/4+1/5+……+1/60+2/60+……+59/60
1/2+1/3+2/3+1/4+2/4+3/4+1/5+……+1/60+2/60+……+59/60
通过观察分析可得:
当分母是奇数时:
如1/3+2/3=1; (1+2+3+4)/5=2; (1+2+3+4+5+6)/7=3.
当分母是偶数时:
如:1/2; (1+2+3)/4=1+1/2; (1+2+3+4+5)/6=2+1/2.
则有原式=(分母偶数部分)+(分母奇数部分)
=[1+2+...+(60/2-1)+(60/2)*1/2]+[1+2+...+(60/2-1)]
=(1+...+29)+30*1/2+(1+...+29)
=(1+29)*29/2+15+(1+29)*29/2
=885