Hey friends plz help me out in this sum.... i 've been trying it for many hrs but i cud not find the exact method of approach.....
Tr = r1-3r2+r4, then
Lim <summation>Tr ( from r=1 to n)
n→∞
I tried to do tis sum by breaking the exp into two terms i.e., in the form of 1/a - 1/b.... but unsuccessful in my attempt.... plz help me...
(sorry latex is not working in my system...)
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1 Answers
341T_r = \frac{r}{1-3r^2+r^4} = \frac{r}{(r^2-1)^2-r^2} = \frac{r}{(r^2+r-1)(r^2-r-1)}
\frac{1}{2} \left[\frac{1}{r^2-r-1} - \frac{1}{r^2+r-1}\right] = \frac{1}{2} \left[ \frac{1}{(r-1)^2+(r-1)-1} - \frac{1}{r^2+r-1} \right]
= f(r-1)-f(r) where f(r)=\frac{1}{2(r^2-r-1)}
and you have your Telescopic Summation
