1/(1×3×5)+1/(3×5×7)+1/(5×7×9)+1/(7×9×11)+1/(9×11×13)的简便算法
题目
1/(1×3×5)+1/(3×5×7)+1/(5×7×9)+1/(7×9×11)+1/(9×11×13)的简便算法
答案
1/(1×3×5)+1/(3×5×7)+1/(5×7×9)+1/(7×9×11)+1/(9×11×13)=(1/2)*[1/(1*3)-1/(3*5)]+(1/2)*[1/(3*5)-1/(5*7)]+...+(1/2)*[1/(9*11)-1/(11*13)]=(1/2)*[1/(1*3)-1/(11*13)]=(1/2)*(140/429)=70...
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