题目写错，应该是：
1/3+1/8+1/15+1/24+...+1/n(n+2)
2/n(n+2)=1/n-1/(n+2)
1/3+1/8+1/15+1/24+...+1/n(n+2)
={[1-1/3]+[1/3-1/5]+[1/5-1/7]+……+[1/n-1/(n+2)]/2
=[1-1/(n+2)]/2=(n+1)/(2n+4)
1/3+1/8+1/15+1/24+...+1/n(n+2)=[1-1/3]+[1/3-1/5]+[1/5-1/7]+……+[1/n-1/(n+2)]/2 =[1-1/(n+2)]/2=(n+1)/(2n+4)
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