2

$r$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.

Siong Thye Goh
  • 149,520
  • 20
  • 88
  • 149
Aurojeet Jena
  • 73
  • 1
    If you're having trouble with formatting, you can consult https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference. For a more short term solution, you could give an online editor a shot, for instance https://www.codecogs.com/latex/eqneditor.php Your question seems fairly unintelligible right now. – Reveillark Aug 02 '17 at 03:25
  • Hey no need to bother , I have solved it .Thanks for your time. – Aurojeet Jena Aug 02 '17 at 03:43
  • 2
    @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. – cdamle Aug 02 '17 at 04:02

1 Answers1

0

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.

Aurojeet Jena
  • 73