设a1=5 an+1=2an+3^n(n≥1) 求an通项,我是新手啦.
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设a1=5an+1=2an+3^n(n≥1)求an通项,我是新手啦.设a1=5an+1=2an+3^n(n≥1)求an通项,我是新手啦.设a1=5an+1=2an+3^n(n≥1)求an通项,我是新手
设a1=5 an+1=2an+3^n(n≥1) 求an通项,我是新手啦.
设a1=5 an+1=2an+3^n(n≥1) 求an通项,我是新手啦.
设a1=5 an+1=2an+3^n(n≥1) 求an通项,我是新手啦.
a(n+1)=2an+3^n
a(n+1)/2^(n+1)=an/2^n+(3/2)^n,(二边同除以2^(n+1))
设bn=an/2^n
那么有b(n+1)-bn=(3/2)^n
bn-b(n-1)=(3/2)^(n-1)
...
b2-b1=(3/2)^1
各式相加得:
bn-b1=(3/2)*[1-(3/2)^(n-1)]/(1-3/2)=-3[1-(3/2)^(n-1)]
b1=a1/2=5/2
所以,bn=5/2-3+3*(3/2)^(n-1)=-1/2+2*3^n/2^n
即an=bn*2^n=-2^(n-1)+2*3^n
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