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
问题描述：
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
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