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I have been trying to solve Summation as Limit to Infinity type of questions but there are hardly a few examples I could find in my book
I know the general method for [tex]\lim_{n \rightarrow \infty } \frac{1}{n}\Sigma_{r=A(x)}^{B(x)}f\frac{r}{n}[/tex] where r/n is replaced by x and 1/n by dx, the limits adjusted and integrated.
However, i am unable to understand how to apply this method if the function is f(r) and not of f(r/n)
Eg. [tex] t_r=\frac{r}{1-3r^2+r^4}, \Sigma_{r=1}^{n} t_r = ? [/tex]
Could someone please explain this method or point me to some resources regarding this.
Thanks
PS: Convergence/Divergence isn't a part of my syllabus, yet.
I know the general method for [tex]\lim_{n \rightarrow \infty } \frac{1}{n}\Sigma_{r=A(x)}^{B(x)}f\frac{r}{n}[/tex] where r/n is replaced by x and 1/n by dx, the limits adjusted and integrated.
However, i am unable to understand how to apply this method if the function is f(r) and not of f(r/n)
Eg. [tex] t_r=\frac{r}{1-3r^2+r^4}, \Sigma_{r=1}^{n} t_r = ? [/tex]
Could someone please explain this method or point me to some resources regarding this.
Thanks
PS: Convergence/Divergence isn't a part of my syllabus, yet.