1 + 10 + 100 + ... = -1/9
July 27, 2011 6:45 AM Subscribe
Mathfilter: In Gelfand's exceptional Algebra
text, he is talking about the formula 1 + x + x^2 + x^3 + ... = 1/(1 - x). He uses the Achilles racing the tortoise model when first introducing the formula. He discusses the case x = 10, whence 1 + 10 + 100 + 1000 + ... = -1/9.
posted by wittgenstein to Education (8 answers total) 4 users marked this as a favorite
Then he says the following: "Is it possible to give a reasonable interpretation of the (absurd) statement 'Achilles will meet the turtle after running -1/9 meters?' (Hint: Yes, it is.) "
I have puzzled over this for awhile and am not sure what he had in mind. Does the hive mind have any ideas?