已知数列{an}满足a1=4,a(n+1)an+6a(n+1)-4an-8=0,记bn=6/an-2,n属于N*(1)求
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已知数列{an}满足a1=4,a(n+1)an+6a(n+1)-4an-8=0,记bn=6/an-2,n属于N*(1)求数列{bn}通项公式
已知数列{an}满足a1=4,a(n+1)an+6a(n+1)-4an-8=0,记bn=6/an-2,n属于N*
(1)求数列{bn}通项公式(2)求数列{an·bn}的前n项和Sn
已知数列{an}满足a1=4,a(n+1)an+6a(n+1)-4an-8=0,记bn=6/an-2,n属于N*
(1)求数列{bn}通项公式(2)求数列{an·bn}的前n项和Sn
![已知数列{an}满足a1=4,a(n+1)an+6a(n+1)-4an-8=0,记bn=6/an-2,n属于N*(1)求](/uploads/image/z/15283660-4-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D4%2Ca%28n%2B1%29an%2B6a%28n%2B1%29-4an-8%3D0%2C%E8%AE%B0bn%3D6%2Fan-2%2Cn%E5%B1%9E%E4%BA%8EN%2A%281%29%E6%B1%82)
n=6/(an-2),an=(6/bn)+2 a(n+1)=(6/b(n+1))+2,b1=3
把an=(6/bn)+2 a(n+1)=(6/b(n+1))+2代入a(n+1)an+6a(n+1)-4an-8=0化简得
3+4bn=4b(n+1) 即4(bn+1)=b(n+1)+1
bn+1为b1+1为首,4为公比的等比数列
bn+1=(b1+1)*4^(n-1)
bn=4^n-1
an*bn=6+2bn=2*4^n+4
Sn=4n+2*4*(1-4^n)/(1-4)=4n+8/3*(4^n-1)
把an=(6/bn)+2 a(n+1)=(6/b(n+1))+2代入a(n+1)an+6a(n+1)-4an-8=0化简得
3+4bn=4b(n+1) 即4(bn+1)=b(n+1)+1
bn+1为b1+1为首,4为公比的等比数列
bn+1=(b1+1)*4^(n-1)
bn=4^n-1
an*bn=6+2bn=2*4^n+4
Sn=4n+2*4*(1-4^n)/(1-4)=4n+8/3*(4^n-1)
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