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数列{an},a1+a2+...+an=3n^2,求an求数列和3/2+4/2^2+5/2^3+...+[n+2]/2^n
题目详情
数列{an},a1+a2+...+an=3n^2,求an
求数列和3/2+4/2^2+5/2^3+...+[n+2]/2^n
求数列和3/2+4/2^2+5/2^3+...+[n+2]/2^n
▼优质解答
答案和解析
1.Sn=3n^2 Sn-1=3n^2-6n+3
Sn-Sn+1=an=6n-3
2.Sn=3/2+4/2^2+5/2^3+...+[n+2]/2^n
2Sn=3/2^2+4/2^3...+(n+1)/2^n+(n+2)/2^(n+1)
Sn-2Sn=-Sn={4-1/2^(n-1)}/2-(n+2)/2^(n+1)
Sn=(n+2)/2^(n+1)+1/2^n-2
Sn-Sn+1=an=6n-3
2.Sn=3/2+4/2^2+5/2^3+...+[n+2]/2^n
2Sn=3/2^2+4/2^3...+(n+1)/2^n+(n+2)/2^(n+1)
Sn-2Sn=-Sn={4-1/2^(n-1)}/2-(n+2)/2^(n+1)
Sn=(n+2)/2^(n+1)+1/2^n-2
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