作业帮1/2+1/6+1/12+1/20+······+1/72+1/90）（计算）就计算过程和思考的办法!
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/13 10:19:54
1/2+1/6+1/12+1/20+······+1/72+1/90）（计算）就计算过程和思考的办法!
1/2+1/6+1/12+1/20+······+1/72+1/90）（计算）
就计算过程和思考的办法!
1/2+1/6+1/12+1/20+······+1/72+1/90）（计算）就计算过程和思考的办法!
1/2+1/6+1/12+1/20+······+1/72+1/90）
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4+.+1/9-1/10
=1-1/10
=9/10;
如果本题有什么不明白可以追问,
这是一个特殊的题型，可以记住。 望采纳，谢谢。
1/2+1/6+1/12+1/20+······+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5...........+1/8-1/9+1/9-1/10
=1-1/10
=9/10
就是裂项，将分数写成两个分数的和
1/2+1/6+1/12+1/20+······+1/72+1/90
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1-1/10
=9/10
答：
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/8-1/9)+(1/9-1/10)
=1-1/10
=9/10
就是裂项求和
原式=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1-1/10
=9/10