UC知道计算：2/6+2/12+2/20+2/30+2/42+2/56+2/72+2/90
来源：百度知道 编辑：UC知道 时间：2024/05/28 18:08:51
有什么简便的方法吗？
2/6+2/12+2/20+2/30+2/42+2/56+2/72+2/90
=2/2-2/3+2/3-2/4+2/4-2/5+2/5-2/6+2/6-2/7+2/7-2/8+2/8-2/9+2/9-2/10
=2/2-2/10=4/5
1/（x+(x+1)）=（1/x）-（1/(x+1)）
2/6+2/12+2/20+2/30+2/42+2/56+2/72+2/90
=2(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=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)]
=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)
=2(1/2-1/10)
=2*2/5
=4/5