January 18th, 2018, 10:11 PM  #1 
Senior Member Joined: Jul 2011 Posts: 402 Thanks: 16  exponential limit
finding $\displaystyle \displaystyle \lim_{n\rightarrow \infty}\frac{a^n}{n!}, a>0$

January 19th, 2018, 12:32 AM  #2  
Senior Member Joined: Oct 2009 Posts: 712 Thanks: 238  Quote:
$$\sum_{n=0}^{+\infty} \frac{a^n}{n!}$$ converges. This is in fact rather easy by the ratio test. What does that then imply about the sequence?  

Tags 
exponential, limit 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
upper limit = lower limit implies convergence  zylo  Calculus  13  May 31st, 2017 01:53 PM 
Exponential limit  panky  Calculus  9  May 26th, 2016 08:08 PM 
Limit of exponential function  Imaxium  Calculus  2  September 4th, 2013 08:56 PM 
Exponential limit!  matemego  Calculus  10  August 24th, 2012 03:06 AM 
exponential function limit problem  rustyjoker  Calculus  9  February 1st, 2012 06:16 AM 