已知数列an前n项和为Sn,且满足4(n+1)(Sn+1)=(n+2)^2an(n属于正整数) 求an
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已知数列an前n项和为Sn,且满足4(n+1)(Sn+1)=(n+2)^2an(n属于正整数) 求an
只要做第2问求an就行
只要做第2问求an就行
(2)
a1=8
4(n+1)(Sn+1)=(n+2)^2.an
Sn+1 = (n+2)^2.an / [4(n+1) ] (1)
S(n-1)+1 = (n+1)^2.a(n-1) / (4n) (2)
(1)-(2)
an = (n+2)^2.an / [4(n+1) ] - (n+1)^2.a(n-1) / (4n)
4n(n+1)an = n.(n+2)^2an - (n+1)^3.a(n-1)
n[ (n+2)^2-4(n+1) ] .an = (n+1)^3.a(n-1)
n^3.an = (n+1)^3.a(n-1)
an/a(n-1) = [(n+1)/n]^3
an/a1 = [(n+1)/2]^3
an = (n+1)^3
a1=8
4(n+1)(Sn+1)=(n+2)^2.an
Sn+1 = (n+2)^2.an / [4(n+1) ] (1)
S(n-1)+1 = (n+1)^2.a(n-1) / (4n) (2)
(1)-(2)
an = (n+2)^2.an / [4(n+1) ] - (n+1)^2.a(n-1) / (4n)
4n(n+1)an = n.(n+2)^2an - (n+1)^3.a(n-1)
n[ (n+2)^2-4(n+1) ] .an = (n+1)^3.a(n-1)
n^3.an = (n+1)^3.a(n-1)
an/a(n-1) = [(n+1)/n]^3
an/a1 = [(n+1)/2]^3
an = (n+1)^3
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