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an=Sn-S(n-1)=-2an+2a(n-1)
3an=2a(n-1)
an/a(n-1)=2/3
等比数列,公比=2/3
S1=2-2a1=a1,
a1=2/3
an=a1*q^(n-1)=(2/3)^n
anSn=(2/3)^n *(2-2*(2/3)^n)
=2(2/3)^n-2(2/3)^(2n)
=(4/3)(2/3)^(n-1)-(8/9)(4/9)^(n-1)
Wn=[(4/3)((2/3)^n-1)/((2/3)-1)]-[(8/9)((4/9)^n-1)/((4/9)-1)]
=4-4(2/3)^n+(8/5)(4/9)^n-(8/5)
=(12/5)-4(2/3)^n+(8/5)(4/9)^n
1年前
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