\lim_{n\rightarrow \infty }\prod_{r=2}^{r=n}{\frac{r^{3}-1}{r^{3}+1}}
-
UP 0 DOWN 0 1 3
3 Answers
62write this as
Î (r-1)(r^2+r+1)(r+1)(r^2-r+1)
= Î (r-1)(r+1) Î {r(r+1)+1}{(r-1)r+1}
if f(r) = (r-1)r+1
The given expression becomes 1/3.2/4.3/5.4/6......... x f(2)/f(1).f(3)/f(2)......
= 1/2 / f(1) = 1/2