58问答库 > 1⼀3+1⼀15+1⼀35+1⼀63用简便方法怎么做？

1⼀3+1⼀15+1⼀35+1⼀63用简便方法怎么做？

2025-04-07 06:29:34
推荐回答（3个）
回答（1）：

=1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)
=1/2×(1-1/3)+1/2×(1/3-1/5)+1/2×(1/5-1/7)+1/2×(1/7-1/9)
=1/2×[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)]
=1/2×(1-1/9)
=4/9

回答（2）：

=1/3 + （1/3-1/5）/2+（1/5-1/7）/2+（1/7-1/9）/2
=1/3+（1/3-1/9）/2
=1/3+1/9
=4/9

回答（3）：

原式=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9)
=1/2*(1-1/9)
=1/2*8/9
=4/9

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