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Question Number 160928 by mnjuly1970 last updated on 09/Dec/21
calculateΩ=∑∞n=1ζ(1+n)−1n+1=?1−γ−−−−−−−−−−−
Answered by qaz last updated on 09/Dec/21
∑∞n=1ζ(1+n)−1n+1=∑∞n=1∑∞k=21k1+n(1+n)=∑∞k=2∑∞n=21nkn=∑∞k=2(∑∞n=1(1nkn)−1k)=∑∞k=2(lnkk−1−1k)=limN→∞∑Nk=1(ln(k+1)−lnk−1k+1)=limN→∞(ln(N+1)−HN+1+1)=1−γ
Commented by mnjuly1970 last updated on 09/Dec/21
bravosirqaz
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