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.
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.
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.