Hi all, I tried to do this limit, but didn't find a way:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\lim_{n \rightarrow \infty} \left( 1 - \frac{1}{2^2} \right) \left( 1 - \frac{1}{3^2} \right) ... \left( 1 - \frac{1}{n^2} \right)

[/tex]

I tried to use theorems I know so far, but it didn't lead to success. Will somebody help how to do these kinds of limits (I know there is no general rule, just some advice what should I try when I'm asked to find limits of such sequences)

The same case is with:

[tex]

\lim_{n \rightarrow \infty} \left( \frac{1}{n} - \frac{2}{n} + \frac{3}{n} - ... + \frac{(-1)^{n-1}n}{n} \right)

[/tex]

or

[tex]

\lim_{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{k(k + 1)}

[/tex]

I hope I will be able to go on with a small hint....

Thank you.

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# How to do this limit?

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