简便运算题:1⼀20+1⼀30+1⼀42+1⼀56+1⼀72

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2025-01-07 15:49:30
推荐回答(2个)
回答1:

=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/4-1/9
=5/36

回答2:

20=4*5 1/20=1/4-1/5
30=5*6 1/30=1/5-1/6
42=6*7 1/42=1/6-1/7
56=7*8 1/56=1/7-1/8
72=8*9 1/72=1/8-1/9
1/20+1/30+1/42+1/56+1/72=(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)=1/4+(-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8)-1/9
=1/4-1/9=5/36