As can be seen, the error grows with n on Gosper's. A correction akin to the following improves it:
- new=orig*k, k=(n/7)^k0
I cannot easily paste the result from Excel, but the error is reduced substantially. Of course such a "correction" is purely empirical, not theoretical. I have the Pari code. I don't think the error ever surpasses the original, but the error sign will alternate some.
--Bill McEachen 22:57, 15 August 2014 (UTC)