Question

( lim _{n rightarrow infty} prod_{r=3}^{n} frac{r^{3}-8}{r^{3}+8}=lim _{n rightarrow infty} prod_{r=3}^{n} frac{(r-2)left(r^{2}+4+2 rright)}{(r+2)left(r^{2}+4 cdot-2 rright)} )
Applying limpt ( rightarrow ) last tem ( rightarrow 1 )
( begin{aligned} lim _{n rightarrow infty} prod_{r=1}^{n} frac{r^{3}-8}{r^{3}+8} &=[1 times 2 times 8 times 4] timesleft[frac{1}{7} times frac{1}{12}right] &=frac{2}{7} end{aligned} )

# nr 8 Ex.11 Evaluate lim 1138, where II represents the product of function. n->

Solution