Tn=(2n-1)/(2^n) 若Tn
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Tn=(2n-1)/(2^n) 若Tn
Cn = 1/2^1 + 3/2^2 + 5/2^3 + …… +(2n-3)/2^(n-1) + (2n-1)/2^n
2Cn =1/2^0 + 3/2^1 + 5/2^2 + 7/2^3 + …… + (2n-1)/2^(n-1)
两式相减,得:
Cn = 1/2^0 + 2/2^1 + 2/2^2 + 2/2^3 + 2/2^(n-1) - (2n-1)/2^n
= 1 + [1 + 1/2 + 1/4 + …… + 1/2^(n-2)] - (2n-1)/2^n
= 1 + 2 - 1/2^(n-2) - (2n-1)/2^n
= 3 - (2n+3)/2^n
< 3
∴c≥3,c(min) = 3
2Cn =1/2^0 + 3/2^1 + 5/2^2 + 7/2^3 + …… + (2n-1)/2^(n-1)
两式相减,得:
Cn = 1/2^0 + 2/2^1 + 2/2^2 + 2/2^3 + 2/2^(n-1) - (2n-1)/2^n
= 1 + [1 + 1/2 + 1/4 + …… + 1/2^(n-2)] - (2n-1)/2^n
= 1 + 2 - 1/2^(n-2) - (2n-1)/2^n
= 3 - (2n+3)/2^n
< 3
∴c≥3,c(min) = 3
已知Sn=1/2n(n+1),Tn=S1+S2+S3+.+Sn,求Tn.
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