Monday, 3 June 2019

real analysis - Necessary and sufficient condition for the existence of $lim_{ntoinfty} a_n$

Let {$a_n$} be a sequence of real numbers. Then what should be a necessary and sufficient condition for the existence of $\lim_{n\to\infty} a_n$?



P.S.- The condition should be in terms of existence of other limits, for example, it exists if $\lim_{n\to\infty} a_{2n}$ and $\lim_{n\to\infty} a_{3n}$ both exist, say...

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...