计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+……+1/6+…+59/60

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 14:03:07
计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+……+1/6+…+59/60
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计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+……+1/6+…+59/60
计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+……+1/6+…+59/60

计算:1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+……+1/6+…+59/60
1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+……+1/6+…+59/60
=1/2+(1+2)/3+(1+2+3)/4+...+(1+2+...+59)/60
=1/2+(1+2)*2/(2*3)+(1+3)*3/(2*4)+...+(1+59)*59/(2*60)
=1/2+2/2+3/2+...+59/2
=(1+2+3+...+59)/2
=(1+59)*59/(2*2)
=15*59
=885

1/(n+1)+2/(n+1)+......+n/(n+1)=(1+2+......+n)/(n+1)=n/2
原式=1/2+2/2+3/2+......+59/2
=(1+2+3+.....+59)/2
=885

1/2+(1-2/3)+2/3+(1-3/4)+2/4+3/4+...+(1-59/60)+(1-58/60)+...+58/60+59/60=1/2+2/2+3/2+4/2+...+ 59/60=1/2(1+2+3+4+...+59)=885