奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+1/99)要有计算过程
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奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+1/99)要有计算过程
奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+
1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+1/99)要有计算过程
奥数六年级1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+1/2/(1+1/2)+1/3/(1+1/2)(1+1/3)+1/4/(1+1/2)(1+1/3)(1+1/4)+.+1/99/(1+1/2)(1+1/3)+...+(1+1/99)要有计算过程
你假设1/2+1/3+1/4+...+1/99=a
那么
(1/2+1/3+1/4+...+1/100)X(1+1/2+1/3+...+1/99)-(1+1/2+1/3+...+1/99+1/100)X(1/2+1/3+1/4+...+1/99)
=（a+1/100）（1+a）-（1+a+1/00）a
展开 =a^2+a+a/100+1/100-a^2-a-a/100
=1/100
所以上题结果为1/100
你题目有误吧？可能漏了括号。 应该是1/2/(1+1/2)+1/3/[(1+1/2)(1+1/3)]+1/4/[(1+1/2)(1+1/3)(1+1/4)]+....+1/99/[(1+1/2)(1+1/3)+...+(1+
=2[1/(2×3)+1/(3×4)+1/(4×5）+...+1/(99×100)]=2(1/2-1/3+1/3-1/4+1/4-1/5...+1/99-1/100)=49/50.其中(1+1/2)(1+1/3)(1+1/4)...(1+1/n)=(3/2)(4/3)...[(n+1)/n]=(n+1)/2.