# Thread: 2 limit of product problems

1. ## 2 limit of product problems

$\lim_{x \mapsto \infty }(\frac{1}{n}\prod_{k=2}^{n}\frac{k^{3}-1}{k^{3}+1}sin\frac{n^{2}}{\pi })$

$\lim_{x \mapsto \infty }(\prod_{k=2}^{n}\frac{(k-1)(k+1)}{k(k+2)}cos\frac{n! + 100}{n^{2}} )$

anyone knows how to solve these two ?

2. ## Re: 2 limit of product problems

For the first, the product is $\leq 1$ and for the second, it's telescopic.

3. ## Re: 2 limit of product problems

x -> infinity but neither expression has x... is it n that should approach infinity?

4. ## Re: 2 limit of product problems

yeah, its n, sorry about that, its a mistake.
@girdav maybe procedure?

5. ## Re: 2 limit of product problems

Where are you stuck?

6. ## Re: 2 limit of product problems

well, I know that i must develop product, so when i do it, then cancel whats possible in nominator and denominator, and lets say i had left some for etc (n+1)/(n+2), what shoud i do with cos (n!+100)/n^2 ?, or in the 1st problem, when i develop product, and cancel whats possible, what to do with sin(...) ?