Author: David Hanley
Date: 16:28:51 12/19/01
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On December 19, 2001 at 16:57:46, Michel Langeveld wrote: >Problem = 1 - ( 16777216! / (16746008! * 16777216 ^ 31208) ) Well, let's see. 16777216! / 16746008! = 16777216 * 16777215 * 16777214 * ..... * 16746009 Because the rest of the factorial cancels out--see? So, we need to divide that by 16777216 ^ 31208 16777216 * 16777215 * 16777214 * ..... * 16746009 -------------------------------------------------- 16777216 ^ 31208 Now, i notice the number of terms in the top is equal to the number of terms in the bottom, once you expand the exponent, but except the first term, the bottom terms are larger, in an increasing fashion. Therefore, the bottom will dominate the top, making the whole fraction very very tiny.. See: 16777216 * 16777215 * 16777214 * ..... * 16746009 -------------------------------------------------- 16777216 * 16777216 * 16777216 * ..... * 16777216 which is like: 16777216 16777215 16777214 ..... 16746009 -------- * -------- * -------- * ----- * -------- 16777216 16777216 16777216 ..... 16777216 A lot of the fractions are close to one, but when you multiply them all out, they're very very nearly zero. so 1 - fraction will be very nearly one. dave
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