Hi everyone,

This is a question I had thought about after we had learnt about limits of a sequence.

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

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

Thank you.

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- Mar 20th 2010, 05:58 PMSudharakaProblem on limits of a sequence.
Hi everyone,

This is a question I had thought about after we had learnt about limits of a sequence.

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

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

Thank you. - Mar 20th 2010, 06:25 PMTKHunny
Are you sure you're not missing a summation in there?

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

The terms are decreasing.

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

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