100分闯关期末冲刺5年级数学(上)1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=多少?1/15+1/35+1/63+1/99+1/143+1/195=多少?

问题描述:

100分闯关期末冲刺5年级数学(上)
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=多少?
1/15+1/35+1/63+1/99+1/143+1/195=多少?

1/2+1/6+1/12+1/20+1/30+1/42+1/56+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)
=1-1/2+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
/(1*2)=1/1-1/2=1-1/2
1/(2*3)=1/2-1/3
1/(3*4)=1/3-1/4
以此类推,每项的第2式和下一项的第1式刚好互为相反数,最后化简,只剩下第1项“1”和最后一项“-1/10”,相减得9/10

第几页?

1/1*2 +1/2*3 +……+1/9*10
=1-1/2+1/2-1/3+……-1/10
=9/10
1/3*5+1/5*7+……+1/13*15
=1/2 *(1/3-1/5+1/5-1/7+……-1/15)
=7/15