You’re so close to getting it it’s funny. If you continued this process infinitely it would in fact approach $2, not infinity.Half its price is $0.50, so it costs 1 + 0.50 = 1.50. However now its price is 1.50, so half its price is 0.75. So now it costs 1+0.75=1.75. However now its price is 1.75.
The book costs infinite money.