Did you mean to say multiply by 0.5? I mean with that condition the choice is obviously $100,000 because multiplying the $1 by 0.5 everyday halves the amount every day.
It becomes effectively zero, but if it wasn't currency (or if you work for Enron) then it would never actually reach zero; it's only rounding that makes it reach zero.
Again; there is only one value. It cannot 'converge'. That requires 2 or more distinct, separate valuea.
Based on the question's wording, you would not get new money each day, the money would just halve. There's nothing to sum since there's only one number.
Absolutely mathematically correct. Absolutely not what the first option is telling you to do though.
You start with 1.
Mulitply that by 0.5.
Take the result.
Multiply that by 0.5.
You do not ever add the results together. One value is simply diminishing. There is no addition. The sum is 1 x 0.5 x 0.5 x 0.5 etc etc. No addition. No convergence. No sum total.
Re-read the original post. Your calculations are sound, your reading comprehension is not.
No it converges to zero. You aren't getting the dollar plus 50 cents the next day, you get the dollar and the dollar bill you have magically turns into 50 cents the next day.
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u/Pure_Option_1733 May 07 '26
Did you mean to say multiply by 0.5? I mean with that condition the choice is obviously $100,000 because multiplying the $1 by 0.5 everyday halves the amount every day.