沙哈拉鸵鸟
幼苗
共回答了16个问题采纳率:100% 举报
Sn
=C1+C2+C3+.Cn
=1*2^(-1)+1+2*2^0+2+3*2^1+3+.+n2^(n-1)+n
=1*2^(-1)+2*2^0+3*2^1+.+n2^(n-1)+1+2+.+n
=1*2^(-1)+2*2^0+3*2^1+.+n2^(n-1)+n(n+1)/2
令Tn=1*2^(-1)+2*2^0+3*2^1+.+n2^(n-1)
2Tn=1*2^0+2*2^1+3*2^2+.+(n-1)2^(n-1)+n2^n
Tn-2Tn=-Tn
=1*2^(-1)+2^0+2^1+2^2+.+2^(n-1)-n2^n
=1/2 +1*(2^n-1)/(2-1)-n2^n
=1/2+2^n-1-n2^n
=-(n-1)2^n-1/2
∴Tn=(n-1)2^n+1/2
∴Sn=(n-1)2^n+1/2+n(n+1)/2
1年前
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