Re: Approximating ,, e"= Napier's constant

From: The Last Danish Pastry (clivet_at_gmail.com)
Date: 07/27/04 

Date: Tue, 27 Jul 2004 14:25:57 +0100

"Alex.Lupas" <alexandru.lupas@ulbsibiu.ro> wrote in message
news:117ac0e5.0407270500.1fbede12@posting.google.com...

> Suppose that T(-1)=7 , T(0)=71 and
>
> T(k+1)=(4k+14)*T(k) +T(k-1) for k=0,1,... .
>
> Define the sequence (E(n))_{n=0,1,...} by
>
> 193 (-1)^k
> E(n) = --- + 2*SUM_{k=0 to k=n} ----------- .
> 71 T(k)T(k+1)
>
> It's true that for n large
>
> E(n) =approx.= e (Napier's constant) ?

Yes. For large n, E(n) is approximately e. The fourth decimal place (and
beyond) is always wrong. But it is approximately e. 

-- 
Clive Tooth
http://www.clivetooth.dk