根据下面的规律试着快速计算1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/901/6=1/2*3=1/2-1/3 1/12=1/3*4=1/3-1/41/20=1/4*5=1/4-1/5…
网友回答
裂项相消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+1/9-1/10 相邻两项抵消
=1/2-1/10
=2/5======以下答案可供参考======
供参考答案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 + 1/4-1/5 + 1/6-1/5 + 1/6-1/7 + 1/7-1/8 + 1/8-1/9 + 1/9-1/10
= 1/2-1/10 = （5-1）/10 = 4/10 = 2/5