To be fair, the author says that the value is between 0 and 1 since _the alternating series clearly converges_ to a value between the 1st and 1st+2nd. So in re

To be fair, the author says that the value is between 0 and 1 since _the alternating series clearly converges_ to a value between the 1st and 1st+2nd. So in reality it explains pretty well why it's between 0 and 1, and leaves the "clearly" to something which in his opinion is common knowledge: https://en.wikipedia.org/wiki/Alternating_series_test https://en.wikipedia.org/wiki/Alternating_series_test