Recent content by sillyus sodus

Homework Statement Show that this sum is convergent if and only if k>1 : \sum_{n=1}^{\infty}\frac{1}{n\log{n}\left(\log{\log{n}}\right)^k}The Attempt at a Solution I've applied the Cauchy condensation test, giving: \frac{2^n}{2^n\log{2^n}\left(\log{\log{2^n}}\right)^k}...

I have an answer now, basically because a_n\rightarrow a and f is continuous then f(a_n)\rightarrow f(a), so there exists n bigger than N such that |f(a_n)-f(a)|<\epsilon so then just choose \epsilon = f(a)/2 do some rearranging and the inequality pops out. In other words, f(a_n) is a...

Sorry, sorry, yes there is another condition: f(a)>0

Homework Statement Given a convergent sequence: a_n \rightarrow a and a continuous function: f:\mathbb{R}\rightarrow\mathbb{R} show that there exists an N\in\mathbb{N} such that \forall n>N: f(a_n)\geq\frac{f(a)}{2} Homework Equations Usual definitions for limit of a sequence...