1/3×2/5
=1/3-1/5
同理
1/5×2/7
=1/5-1/7
后面类推得：
所以原式=1/3 × 2/5+1/5 ×2/7+1/7 ×2/9+……1/99 × 2/101
=(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)
=1/3-1/101
=98/303
∵每一项都是1/(2n+1)×2/(2n+3)的形式,n从1~49
1/(2n+1)×2/(2n+3)=1/(2n+1)-1/(2n+3)
1/3*2/5+1/5*2/7+ 1/7*2/9+……+1/99*2/101
8个回答
相关问题
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