1/2+1/(2+3)+1/(2+3+4)+.+1/(2+4+5+...)200)=?

来源：学生作业帮助网 编辑：作业帮 时间：2024/07/11 05:16:41
1/2+1/(2+3)+1/(2+3+4)+.+1/(2+4+5+...)200)=?
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1/2+1/(2+3)+1/(2+3+4)+.+1/(2+4+5+...)200)=?
1/2+1/(2+3)+1/(2+3+4)+.+1/(2+4+5+...)200)=?

1/2+1/(2+3)+1/(2+3+4)+.+1/(2+4+5+...)200)=?
1/2+1/(2+3)+1/(2+3+4)+.+1/(2+3+4+5+...200)
=1/2+1/[2*(2+3)/2]+1/[3*(2+4)/2]+……+1/[199*(2+200)/2]
=1/2+2/(2*5)+2/(3*6)+2/(4*7)+……+2/(199*202)
=1/2+2/3(1/2-1/5)+2/3(1/3-1/6)+2/3(1/4-1/7)+……+2/3(1/199-1/202)
=1/2+2/3(1/2-1/5+1/3-1/6+1/4-1/7+1/5-1/8+……+1/199-1/202)
=1/2+2/3(1/2+1/3+1/4-1/200-1/201-1/202)
=1/2+2/3(13/12-30301/2030100)
=1/2+2/3*2168974/2030100
=1/2+2168974/3045150
=3691549/3045150

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