does anyone know the "card trick" where you have 52 cards and you push the top card out til it tips... which is 1/2 of a card. next you push the second card from the top out til it tips... which you can only push out 1/4 of the way... next push out the third card from the top and it goes ______ until it tips. This book i'm reading says it goes 1/6, but I can't tell how they get it... I keep getting 1/8? Can anyone help me?
Is this the only information they present? It seems like from 1/2 and 1/4, 1/8 and 1/6 would be equally correct.
the context of the problem is showing through example the summation of a harmonic series... they're saying 1/2+1/4+1/6+1/8+1/10+.... +1/n =infinity... i just don't know how they get the harmonic sequence out of the card example... cause to me it would be geometric... meaning 1/2+1/4+1/8+1/16+...+1/n^2 ...which converges... what do you think?
So, basically, to me, two numbers aren't enough to discern a pattern there -- precisely because of the alternative you mention. I'm not sure where they magically derive the conclusion that it would be a harmonic sequence; there just doesn't seem to be enough information to conclude that.
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