1/(1×3×5) +1/(3×5×7)+1/(5 - 知识问答

1/(1×3×5) +1/(3×5×7)+1/(5×7×9)+…+1/(11×13×15)这个式子怎么用简便运算

1个回答

1/(1×3×5) +1/(3×5×7)+1/(5×7×9)+…+1/(11×13×15)
=1/2x[1/1x3-1/3x5]+1/2[1/3x5-1/5x7]+.+1/2[1/11x13-1/13x15]
=1/2[1/1x3-1/3x5+1/3x5-1/5x7+.+1/11x13-1/13x15]
=1/2x[1/1x3-1/13x15]
=1/2x64/195
=32/195

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