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已知数列{an}满足an+1^2+2^2+.n^2,则3/a1+5/a2+7/a3.+21/a10=
题目详情
已知数列{an}满足an+1^2+2^2+.n^2,则3/a1+5/a2+7/a3.+21/a10=
▼优质解答
答案和解析
an=n(n+1)(2n+1)/6,
(2n+1)/an =6/n(n+1)=6[1/n -1/(n+1)],
3/a1+5/a2+7/a3.+21/a10=6[1/1 -1/2 +1/2-1/3+...+1/10-1/11]=6[1-1/11]=60/11
(2n+1)/an =6/n(n+1)=6[1/n -1/(n+1)],
3/a1+5/a2+7/a3.+21/a10=6[1/1 -1/2 +1/2-1/3+...+1/10-1/11]=6[1-1/11]=60/11
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