已知数列{An},An+1=2(n+1)+An,求数列An通向求详解
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已知数列{An},An+1=2(n+1)+An,求数列An通向求详解
已知数列{An},An+1=2(n+1)+An,求数列An通向
求详解
已知数列{An},An+1=2(n+1)+An,求数列An通向求详解
A(n+1)=An+2(n+1)
A(n+1)-An=2(n+1)
即An-A(n-1)=2n
A(n-1)-A(n-2)=2(n-1)
.
A3-A2=2*3
A2-A1=2*2
以上各式相加得:
An-A1=2*(2+3+...+n)=2*(2+n)*(n-1)/2=(n+2)(n-1)
故An=A1+(n+2)(n-1)
题目中是否有A1=?
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