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Question about the integral test 
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#1
Jul2411, 06:45 AM

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1. The problem statement, all variables and given/known data
We have to determine whether [itex]\sum 1/n^2 + 4[/itex] is convergente or divergent 2. Relevant equations I'm trying to work the problem through trigonometric substitution. I was wondering if I could just determine that by the Pseries test, the function 1/n^2 will always be larger than the other one, since p is greater than 1 in this case, both are convergent. 3. The attempt at a solution 


#2
Jul2411, 07:55 AM

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hi salazar888! welcome to pf!
the latter sum converges (from the pseries test), so so must the former (from the direct comparison test) 


#3
Jul2411, 09:45 AM

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Obviously, since the series [itex] \sum \frac{1}{n^2} [/itex] converges, the sum you wrote, [itex] 4 + \sum \frac{1}{n^2}[/itex] converges also.
RGV 


#4
Jul2411, 09:47 AM

P: 12

Question about the integral test
The series 1/n does not converge. It's the harmonic series. You read it wrong. I get what you're saying though.



#5
Jul2411, 10:22 AM

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I saw the error and edited it immediately.
RGV 


#6
Jul2411, 10:24 AM

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[tex]\sum\left(\frac{1}{n^2}+ 4\right)[/tex] does NOT converge! 


#7
Jul2411, 10:53 AM

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I agree, but that is not what he wrote. We all know he meant sum 1/(n^2 + 4), but he wrote sum (1/n^2) + 4, which is very different according to standard math expression padding rules. Since he was using 'tex' anyway, he should have been able to enter "{n^2+4}" as the second argument of the '\frac' command.
RGV 


#8
Jul2411, 11:08 AM

P: 12

Yes it was my fault. I've only been on the forum for a couple of days. Thanks for the help guys. I will improve at typing the commands.



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