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请观察下面等式回答问题:1/(1×3)=1/2(1-1/3),1/(3×5)=1/2(1/3-1/5),1/(5×7)=1/2(1/5-1/7)…,请计算:
(1-1/3)+1/(3×5)+1/(5×7)+…+1/(2n-1)(2n+1)等于多少,要过程哦.
人气:197 ℃ 时间:2020-03-31 04:08:33
解答
原式=1/2(1-1/3+1/3-1/5+1/5…+1/2n-1-1/2n+1)
中间消去
=1/2(1-1/2n+1)
=n/2n+1
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