脱式计算 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8

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脱式计算 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
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脱式计算 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
脱式计算 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8

脱式计算 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
=﹙1-1/2﹚+﹙1/2-1/3﹚+﹙1/3-1/4﹚+﹙1/4-1/5﹚+﹙1/5-1/6﹚+﹙1/6-1/7﹚+﹙1/7-1/8﹚
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
=1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+1/5×1/6+1/6×1/7+1/7×1/8
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

原式=1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8= 1-1/8 = 7/8