Question

递等式计算。

1 简算 1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
2 巧算
1-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-……-(1/9-1/10)

Answer 1

递等式计算怎么算！

Answer 2

1 1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
= 1/2 × 1/3 +1/3×1/4 + 。。。。+1/9×1/10
= 1/2 -1/3 +1/3-1/4+。。。。1/9-1/10
= 1/2 -1/10
= 2/5

2 巧算
1-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-……-(1/9-1/10)
= 1-1/2 +1/3 -1/3 +1/4 -。。。。-1/9 +1/10
= 1-1/2 +1/10
= 3/5

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Answer 3

1原式=1/2-1/3+1/3-1/4+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/2-1/10
=2/5
2,原式=1-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/6......-1/9+1/10
=1/2+1/10
=3/5