用简便方法计算:1/8+1/15+1/24+1/35+···+1/80+1/99

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用简便方法计算:1/8+1/15+1/24+1/35+···+1/80+1/99用简便方法计算:1/8+1/15+1/24+1/35+···+1/80+1/99用简便方法计算:1/8+1/15+1/2

用简便方法计算:1/8+1/15+1/24+1/35+···+1/80+1/99
用简便方法计算:1/8+1/15+1/24+1/35+···+1/80+1/99

用简便方法计算:1/8+1/15+1/24+1/35+···+1/80+1/99
1/8+1/15+1/24+1/35+···+1/80+1/99
=1/2*4+1/3*5+1/4*6+1/5*7+...+1/8*10+1/9*11
=1/2(1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+...+1/8-1/10+1/9-1/11)
=1/2(1/2+1/3-1/10-1/11)
=1/2x(11/15-1/11)
=1/2x106/165
=53/165