原式=7／12 - 9／20 + 11／30 -.....-17／72
=(1／3 + 1／4)-(1／4 + 1／5)+(1／5 + 1／6)....+(1／8 + 1／9)
=1／3 + 1／9
=4／9
5/6=1/2+1/3,7/12=1/3+1/4,同理可得后面的9/20,11/30,13/42,15/56,17/72.所以原式=1-(1/2+1/3)+1/3+1/4……-(1/6+1/7)+1/7+1/8-(1/8+1/9)=7/18
原式=7/12
-
9/20
+
11/30
-.....-17/72
=(1/3
+
1/4)-(1/4
+
1/5)+(1/5
+
1/6)....+(1/8
+
1/9)
=1/3
+
1/9
=4/9
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