![]() |
|
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion |
![]() |
| LinkBack | Thread Tools | Display Modes |
January 18th, 2019, 08:49 AM | #1 |
Senior Member Joined: Dec 2015 From: iPhone Posts: 387 Thanks: 61 | Integer part
How can I find the integer part of $\displaystyle e^e \;$? (without calculator) e - Euler constant What about approximation? First, I tried one example for $\displaystyle 2e$ and $\displaystyle e^2$, to see whether it is possible. $\displaystyle 3>e>\frac{5}{2}\;$ ,then multiply by 2 6>2e>5 so integer part of 2e is 5. Last edited by skipjack; January 19th, 2019 at 12:21 AM. |
![]() |
January 19th, 2019, 12:27 AM | #2 |
Global Moderator Joined: Dec 2006 Posts: 20,298 Thanks: 1971 |
How much basic arithmetic is acceptable, given that use of a calculator isn't allowed? Can you assume that e = 2.718... or does that have to be proved as well?
|
![]() |
January 19th, 2019, 02:01 AM | #3 |
Senior Member Joined: Dec 2015 From: iPhone Posts: 387 Thanks: 61 |
By calculator ,integer part of $\displaystyle e^e$ is 15. But integer part of $\displaystyle {2.7}^{2.7}$ is 14 , same for 2.71 . Last edited by idontknow; January 19th, 2019 at 02:07 AM. |
![]() |
January 19th, 2019, 05:56 AM | #4 |
Global Moderator Joined: Dec 2006 Posts: 20,298 Thanks: 1971 |
$e^{2.71} >15$, but I think a lot of arithmetic is needed to prove that.
|
![]() |
![]() |
|
Tags |
integer, part |
Thread Tools | |
Display Modes | |
|
![]() | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Integer part | Dacu | Algebra | 7 | April 17th, 2015 06:05 AM |
Equation integer part | gerva | Algebra | 18 | January 6th, 2015 07:38 AM |
Integer Part (Geometric interpretation help) | Jakarta | Number Theory | 0 | May 12th, 2013 11:09 AM |
integer part of S | Albert.Teng | Algebra | 2 | September 23rd, 2012 04:46 AM |
More about part integer | Fernando | Number Theory | 1 | April 13th, 2012 07:19 AM |