设数列AN满足A1=2,A(N+1)-AN=3X2^(2N-1)?
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设数列AN满足A1=2,A(N+1)-AN=3X2^(2N-1)?
(1)求数列AN的通项公式
2,令BN=N AN ,求BN前N项和SN
(1)求数列AN的通项公式
2,令BN=N AN ,求BN前N项和SN
![设数列AN满足A1=2,A(N+1)-AN=3X2^(2N-1)?](/uploads/image/z/5805984-48-4.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97AN%E6%BB%A1%E8%B6%B3A1%3D2%2CA%28N%2B1%29-AN%3D3X2%5E%282N-1%29%3F)
a(n+1)-an=3*2^(2n-1)
an-a(n-1)=3*2^(2n-3)
...
a3-a2=3*2^3
a2-a1=3*2^1
相加
an-a1=3[2^1+2^3+2^5+2^7+...+2^(2n-3)]
=3*2*[2^(2n-2)-1]/(2^2-1)
=2^(2n-1)-2
an=a1+2^(2n-1)-2=2^(2n-1)
an=2^(2n-1)
bn=n*2^(2n-1)
an-a(n-1)=3*2^(2n-3)
...
a3-a2=3*2^3
a2-a1=3*2^1
相加
an-a1=3[2^1+2^3+2^5+2^7+...+2^(2n-3)]
=3*2*[2^(2n-2)-1]/(2^2-1)
=2^(2n-1)-2
an=a1+2^(2n-1)-2=2^(2n-1)
an=2^(2n-1)
bn=n*2^(2n-1)
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