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幼苗
共回答了18个问题采纳率:88.9% 举报
(1)
a1=1/2
an=n/2^n a(n-1)=(n-1)/2^(n-1)
an-a(n-1)=[n-2n+2]/2^n=(2-n)/2^n=2/2^n-an
2an-a(n-1)=1/2^(n-1)
2a(n-1)-a(n-2)=1/2^(n-2)
...
2a2-a1=1/2
累加
2Tn-2a1-T(n-1)=1/2+1/2^2+...+1/2^(n-1)
Tn-2a1+an=1/2+1/2^2+...+1/2^(n-1)
Tn=2a1-an+(1/2)[1-(1/2)^(n-1)]/(1-1/2)
=1-n/2^n+1-2/2^n
=2-(n+2)/2^n
(2)
Sn=(1+2+...+n)+(1/2+1/2^2+...+1/2^n)
=n(n+1)/2+(1/2)[1-(1/2)^n](1-1/2)
=n(n+1)/2+1-1/2^n
1年前
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