6年级分数简便运算奥数题

可以变形，把第二位的6看成是2乘以3.后面依次类推。
原式=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6
=1-1/7
=6/7

本题需要变形裂项
原式=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6
=1-1/7
=6/7

(1/2+1/6+1/12+1/20+1/30+1/42)X420/420
=(210+70+35+21+14+10)/420
=360/420
=6/7

1/2+1/6+1/12+1/20+1/30+1/42
=(1-1/2 )+(1/2 -1/3 )+(1/3 -1/4)+(1/4 -1/5 )+(1/5 -1/6 )+(1/6 -1/7)
=1- 1/7
=6/7

2=1*2, *3,12=3*4,20=4*5,30=5*6,42=6*7,
=(1-1/2 )+(1/2 -1/3 )+(1/3 -1/4)+(1/4 -1/5 )+(1/5 -1/6 )+(1/6 -1/7)
=1- 1/7
=6/7 *3,12=3*4,20=4*5,30=5*6,42=6*7,