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April 23rd, 2017, 07:47 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 230 Thanks: 2  Convergence Series
Can anyone let me know Is my assumption of the following series is convergent is true ? $\displaystyle \sum_{i=1}^{\infty} \frac{n^2 + 1}{n^3 + n}$ Many thanks in advance 
April 23rd, 2017, 08:49 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,738 Thanks: 1388 
$\dfrac{n^2+1}{n^3+n} = \dfrac{n^2+1}{n(n^2+1)}=\dfrac{1}{n}$ $\displaystyle \sum_{n=1}^\infty \dfrac{1}{n}$ is the harmonic series which diverges. 
April 23rd, 2017, 08:53 AM  #3  
Senior Member Joined: Nov 2015 From: hyderabad Posts: 230 Thanks: 2  Quote:
Thank you ðŸ˜Š  
April 23rd, 2017, 08:57 AM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,738 Thanks: 1388  Quote:
list of series tests  
April 23rd, 2017, 05:52 PM  #5  
Senior Member Joined: Nov 2015 From: hyderabad Posts: 230 Thanks: 2  Quote: Thanks again!  
April 23rd, 2017, 06:45 PM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,780 Thanks: 1025 Math Focus: Elementary mathematics and beyond 
Try the integral test.

April 23rd, 2017, 06:59 PM  #7 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 230 Thanks: 2  
April 29th, 2017, 12:09 AM  #8  
Senior Member Joined: Nov 2015 From: hyderabad Posts: 230 Thanks: 2  Quote:
Can you help me in understanding its properties like what could be the value of $\infty / \infty$, $\infty * \infty$ or $\infty+ n$ ($n$ is some natural number). Please clarify its values to determine the limit. Thanks in advance!  
April 29th, 2017, 04:57 AM  #9  
Math Team Joined: Jul 2011 From: Texas Posts: 2,738 Thanks: 1388  Quote:
$\infty * \infty = \infty$ $\infty+ n = \infty$ ($n$ is some natural number). Go to the link for further information ... The Algebra of Infinity  

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