User Name Remember Me? Password

 Calculus Calculus Math Forum

 August 18th, 2019, 09:11 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91 Hard problem Evaluate $\displaystyle L(s)=\lim_{n\rightarrow \infty } s^{n} \:$ , $\displaystyle s\in \mathbb{R}^{+}$. August 18th, 2019, 11:08 AM   #2
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,272
Thanks: 942

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 Originally Posted by idontknow Evaluate $\displaystyle L(s)=\lim_{n\rightarrow \infty } s^{n} \:$ , $\displaystyle s\in \mathbb{R}^{+}$.
This is pretty much straightforward so I'm not going to supply a proof, just the answer.
$\displaystyle \lim_{n \to \infty} s^n \to \begin{cases} \infty & 1 < s \\ 1 & 1 = s \\ 0 & 1 > s \end{cases}$

-Dan August 19th, 2019, 06:54 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91 Check this one : $\displaystyle L(s)=s\cdot \lfloor s \rfloor$. L=s[s] . But it is not working for s>1 . Last edited by idontknow; August 19th, 2019 at 07:25 AM. August 19th, 2019, 08:13 AM   #4
Senior Member

Joined: Dec 2015
From: somewhere

Posts: 642
Thanks: 91

Quote:
 Originally Posted by idontknow Check this one : $\displaystyle L(s)=s\cdot \lfloor s \rfloor$. L=s[s] . But it is not working for s>1 .
Assuming $\displaystyle 1/0=\infty$ , the equality holds true .
$\displaystyle L(s)=s\lfloor s \rfloor +\frac{s\lfloor s \rfloor -1}{\lfloor s^{-1} \rfloor }$$\displaystyle \lfloor s \rfloor .$

Last edited by idontknow; August 19th, 2019 at 08:24 AM. August 19th, 2019, 09:14 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 On that assumption, $\displaystyle L(s) = \frac{\lfloor s \rfloor}{\lfloor s^{-1} \rfloor}$ is simpler. Thanks from idontknow Tags hard, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ionika Algebra 0 February 5th, 2014 11:18 AM Cephal Calculus 2 December 27th, 2013 05:18 PM math221 Calculus 8 March 17th, 2013 05:51 PM john mraz Advanced Statistics 0 June 15th, 2010 12:32 AM nguoidep_68 Algebra 3 October 31st, 2007 03:11 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      