1. ## Limit Question

Given that $\Biggl| \cos^{-1} \biggl( \frac{1}{n} \biggr) \Biggr|< \frac{\pi}{2}$ evaluate:

$\lim_{n \to \infty} \frac{2}{\pi} (n+1) \cos^{-1} \biggl(\frac{1}{n} \biggr) -n$

2. Originally Posted by Chandru1
Given that $\Biggl| \cos^{-1} \biggl( \frac{1}{n} \biggr) \Biggr|< \frac{\pi}{2}$ evaluate:

$\lim_{n \to \infty} \frac{2}{\pi} (n+1) \cos^{-1} \biggl(\frac{1}{n} \biggr) -n$
put $n=\sec t.$ then you'll have a simple limit $\lim_{t \to\frac{\pi}{2}}\frac{2t(1+\cos t) - \pi}{\pi \cos t}=1-\frac{2}{\pi},$ by applying L'Hopital once.