■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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