这道题怎么做,求学霸看看 50
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(n+3)/n(n+1)(n+2) = (n+2)/n(n+1)(n+2) +1/n(n+1)(n+2)=1/n(n+1)+1/n(n+1)(n+2);
而1/n(n+1)=1/n-1/n+1,1/n(n+1)(n+2)=1/2n(n+1)-1/2(n+1)(n+2);
所以原式等于3/2n(n+1)-1/2(n+1)(n+2)=3/2n-3/2(n-1)-1/2(n+1)+1/2(n+2)
而对于数列1/n(n+1)=1/n-1/n+1求和得1-1/2+1/2-1/3+...+1/n-1/n+1=1-1/n+1;
同理数列1/(n+1)(n+2)的和为1/2-1/(n+2)
所以原式的和为3/2n(n+1)-1/2(n+1)(n+2)=1.5-3/2(n+1)-1/4+1/2(n+2)=1.25--3/2(n+1)+1/2(n+2)
...这是我从别人那里看到的,摘来的,有结论得,体题中n=8,代入得结果为:4/5,即0.8
而1/n(n+1)=1/n-1/n+1,1/n(n+1)(n+2)=1/2n(n+1)-1/2(n+1)(n+2);
所以原式等于3/2n(n+1)-1/2(n+1)(n+2)=3/2n-3/2(n-1)-1/2(n+1)+1/2(n+2)
而对于数列1/n(n+1)=1/n-1/n+1求和得1-1/2+1/2-1/3+...+1/n-1/n+1=1-1/n+1;
同理数列1/(n+1)(n+2)的和为1/2-1/(n+2)
所以原式的和为3/2n(n+1)-1/2(n+1)(n+2)=1.5-3/2(n+1)-1/4+1/2(n+2)=1.25--3/2(n+1)+1/2(n+2)
...这是我从别人那里看到的,摘来的,有结论得,体题中n=8,代入得结果为:4/5,即0.8
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