$r$th term of a series is $t_r=\frac{r}{1-r^2+r^4}$. Then how do we compute $\lim_{n \to \infty }\sum_{r=1}^n t_r$.

I tried converting the summation into a definite integral so as to use Newton Leibnitz theorem , but was unable to do so. I don't see how to incorporate "$n$" into the general term. Please somebody help. It would be very helpful if someone gives the full solution as I am attempting such a summation - based limit question for the first time.

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    $\begingroup$ If you're having trouble with formatting, you can consult math.meta.stackexchange.com/questions/5020/…. For a more short term solution, you could give an online editor a shot, for instance codecogs.com/latex/eqneditor.php Your question seems fairly unintelligible right now. $\endgroup$ – Reveillark Aug 2 '17 at 3:25
  • $\begingroup$ Hey no need to bother , I have solved it .Thanks for your time. $\endgroup$ – Aurojeet Jena Aug 2 '17 at 3:43
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    $\begingroup$ @AurojeetJena How can you compute that? It is easy to see that the limit has an upper and lower bound. But it is not easy to see its exact value. $\endgroup$ – cdamle Aug 2 '17 at 4:02

First compute the sum of series upto n terms using "Method of Difference" ,then put the value , that includes "n" as variable in the limit.


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