# Problem on limits of a sequence.

• March 20th 2010, 05:58 PM
Sudharaka
Problem on limits of a sequence.
Hi everyone,

Using the definition of limits of a sequence can we disprove that,

$\lim_{n\rightarrow{\infty}}\frac{1}{n^2}=1$

Thank you.
• March 20th 2010, 06:25 PM
TKHunny
Are you sure you're not missing a summation in there?

$\frac{\frac{1}{(n+1)^{2}}}{\frac{1}{n^{2}}}\;=\;\f rac{n^{2}}{n^{2}+OtherStuff}\;<\;1$

The terms are decreasing.

$\frac{1}{2^{2}}\;=\;\frac{1}{4}\;<\;1$

I think we're done as the problem has been posted.