a1=1 S(n+1)=4an+2求an通项
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a1=1 S(n+1)=4an+2求an通项
a1=1 S(n+1)=4an+2
求an通项
a1=1 S(n+1)=4an+2求an通项
因为Sn+1=4an+2
Sn=4an-1 +2
故an+1=4an-4an-1 an+1-2an=2(an-an-1) 令an+1-2an=bn+1
故bn+1=2bn 所以bn=b2*2^(n-2)=(a2-2a1)*2^(n-2)=3*2^(n-1)
所以an-2an-1=3*2^(n-1)
an/2^n-an-1/2^(n-1)=3/2
故令Cn=an/2^n 所以Cn-Cn-1=3/2
累加得 Cn=3/2(n-1) an=3(n-1)2^(n-1) (n≥2) a1=1
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