
an=(2n-1)*2^n求前n项和Sn
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an = n2^(n+1) - 2^n
令bn = n2^(n+1),cn = 2^n
bn的前n项为Bn,cn的前n项为Cn,an的前n项为An,
Bn = 1*2^2+2*2^3+3*2^4+......+n2^(n+1)
2Bn= 1*2^3+2*2^4+.......+(n-1)2^(n+1)+n2^(n+2)
相减:
-Bn = 2^2+2^3+.......+2^(n+1)-n2^(n+2)
=4(2^n - 1)-n2^(n+2)
Bn = (n-1)2^(n+2) + 4
Cn = 2^(n+1)-2
An = Bn + Cn
=(n-1)2^(n+2) +2^(n+1) + 2
令bn = n2^(n+1),cn = 2^n
bn的前n项为Bn,cn的前n项为Cn,an的前n项为An,
Bn = 1*2^2+2*2^3+3*2^4+......+n2^(n+1)
2Bn= 1*2^3+2*2^4+.......+(n-1)2^(n+1)+n2^(n+2)
相减:
-Bn = 2^2+2^3+.......+2^(n+1)-n2^(n+2)
=4(2^n - 1)-n2^(n+2)
Bn = (n-1)2^(n+2) + 4
Cn = 2^(n+1)-2
An = Bn + Cn
=(n-1)2^(n+2) +2^(n+1) + 2
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