eh....
So the first term is approximately sqrt(2), the second term 1/2 of that, then the third term i have no clue wtf is going on....and it goes downhill from there.
It was a specific example they gave for the problem:
Investigate a formula in Finite Differences for transforming a series the terms of
which (at least after a certain number) are alternately positive and negative, and decrease
slowly, into one which is generally much more rapidly convergent.
But yea, currently preoccupied with that series...don't really recognize wtf it's doing. Unless there really is no pattern to it..but that would suck. Though the main problem itself is somewhat interesting too.