1/3+1/8+1/15+1/24……+1/99用简便算法怎么做?

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1/3+1/8+1/15+1/24……+1/99用简便算法怎么做?

1/3+1/8+1/15+1/24……+1/99用简便算法怎么做?
1/3+1/8+1/15+1/24……+1/99用简便算法怎么做?

1/3+1/8+1/15+1/24……+1/99用简便算法怎么做?
上面的回答基本正确,答案再除以2就对了, 36/55

1/3+1/8+1/15+1/24……+1/99
=1/1*3+1/2*4+1/3*5+1/4*6+...+1/9*11
=1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+...+1/9-1/11
=(1-1/3+1/3-1/5+...+1/9-1/11)+(1/2-1/4+1/4-1/6+...+1/8-1/10)
=(1-1/11)+(1/2-1/10)
=10/11+2/5
=72/55