1/4×5+1/5×6+1/6×7+1/7×8=

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1/4×5+1/5×6+1/6×7+1/7×8=1/4×5+1/5×6+1/6×7+1/7×8=1/4×5+1/5×6+1/6×7+1/7×8=1/4×5+1/5×6+1/6×7+1/7×8=1/4-

1/4×5+1/5×6+1/6×7+1/7×8=
1/4×5+1/5×6+1/6×7+1/7×8=

1/4×5+1/5×6+1/6×7+1/7×8=
1/4×5+1/5×6+1/6×7+1/7×8
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/4-1/8
=1/8

1/4*5=1/4-1/5
1/5*6=1/5-1/6
所以上式化为1/4-1/8=1/8

=5/4+6/5+7/6+8/7=4.759

出的有歧义啊 像1/4*5是1除以20的意思 还是1/4在乘以5的意思呢 不严谨

4(319/420)

1/n*(n+1)=1/n-1/(n+1)
所以1/4×5+1/5×6+1/6×7+1/7×8
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/4-1/8
=1/8