查人人中国名人网天生要完美分集剧情:数学高手进来,帮帮忙!
来源：百度文库 编辑：查人人中国名人网 时间：2024/05/03 01:17:27
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…100)
/是分数线
/是分数线
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…100)
=1+1/[(1+2)*2/2]+1/[(1+3)*3/2]+1/[(1+4)*4/2]+...+1/[(1+100)*100/2]
=1+1/(3*2/2)+1/(4*3/2)+1/(5*4/2)+...+1/(101*100/2)
=1+2(1/2*3+1/3*4+1/4*5+...+1/100*101)
=1+2[(3-2)/2*3+(4-3)/3*4+(5-4)/4*5+...+(101-100)/100*101]
=1+2(3/2*3-2/2*3+4/3*4-3/3*4+5/4*5-4/4*5+...+101/100*101-100/100*101)
=1+2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/100-1/101)
=1+2(1/2-1/101)
=1+2*99/202
=1+99/101
=200/101
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+4+…100)
=2[1-1/2]+2[1/2-1/3]+2[1/3-1/4]+...+2[1/100-1/101]
=2[1-1/101]
=2*100/101
=200/101
编程计算：结果为：1.98019801980198
1+2+3+4+…n=n(n+1)/2
1/n(n+1)=1/n-1/(n+1)
200/101