■ガウス・ヒンチン・レヴィ(その8)
幾何平均
{Π(1,n)klog2(1+1/k(k+2))}^1/n=α
{Π(1,n)klog2(1+1/k(k+2))}=α^n
算術平均
1/nΣ(1,n)klog2(1+1/k(k+2))=β
Σ(1,n)klog2(1+1/k(k+2))=βn
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klog2(1+1/k(k+2))
=log2(1+1/k(k+2))^k
1<(1+1/k(k+2))^k(k+2)<e
1<(1+1/k(k+2))^k<e^1/(k+2)
したがって,k→∞のとき,
(1+1/k(k+2))^k→1
klog2(1+1/k(k+2))→0
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[まとめ]これらはこれまでの議論とは別物なのだろうか?
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