2²/1×3+4²/3×5+6²/5×7+…+20²/19×21怎么简算?
2²/1×3+4²/3×5+6²/5×7+…+20²/19×21怎么简算?
数学人气:519 ℃时间:2020-04-30 06:35:12
优质解答
2²/1×3+4²/3×5+6²/5×7+…+20²/19×21=1+1/1x3+1+1/3x5+1+1/5x7+...+1+1/19x21=1x19+1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+...+1/2(1/19-1/21)=19+1/2(1-1/21)=19+10/21=19又10/21
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