数学题简算``

来源：百度知道 编辑：UC知道 时间：2024/05/18 00:57:11
用简便算法算
1/2+ 1/6+1/12+1/20+1/30+1/42+1/56+1/76+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
=1-1/10
=9/10
南师大教过的

1/2+ 1/6+1/12+1/20+1/30+1/42+1/56+1/76+1/90

=1/1*2+1/2*3+1/3*4+...+1/9*10

=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10

=1-1/10

=9/10

1/2+ 1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=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)
=(1-1/2)+(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) 去括号,抵消掉了,剩下1,1/10
=1-1/10
=9/10

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)=1/2+1/3-1/2+1/4-1/3+1/5-1/4+1/6-1/5+1/7-1/6+1/8-1/7+1/9-1/8+1/10-1/9=1/10