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 Jun 11 awarded Popular Question Jan 23 comment A proof to the theorem: $\{s_n\}_n\subset\mathbb{R}$ is convergent if it is cauchy sequence. @Freddy, i think considering increasing or decreasing is not work as a sequence may converge to a point with oscillating between positive and negative values. So may be what you mean is considering the sequence $\{t_m\}_m$ where $t_m=|s_m|$ right? Jan 23 comment A proof to the theorem: $\{s_n\}_n\subset\mathbb{R}$ is convergent if it is cauchy sequence. @IttayWeiss Oh, i see the problem, i should rather prove it converges to $\limsup$ instead of $\sup$, is it better now??? Jan 23 revised A proof to the theorem: $\{s_n\}_n\subset\mathbb{R}$ is convergent if it is cauchy sequence. added 16 characters in body Jan 23 comment A proof to the theorem: $\{s_n\}_n\subset\mathbb{R}$ is convergent if it is cauchy sequence. @IttayWeiss ya, i mean the idea Jan 23 asked A proof to the theorem: $\{s_n\}_n\subset\mathbb{R}$ is convergent if it is cauchy sequence. Jan 20 asked Reference books or any sources advice for my advanced calculus course Jan 17 comment find all sequence satisfies $y^n_1 + 2y^n_2 + · · · + 2011y^n_{2011} = a^{n+1}+1$ @HaraldHanche-Olsen I am not sure. This is a question from my friend. Jan 17 awarded Editor Jan 17 revised find all sequence satisfies $y^n_1 + 2y^n_2 + · · · + 2011y^n_{2011} = a^{n+1}+1$ deleted 1 characters in body Jan 17 asked find all sequence satisfies $y^n_1 + 2y^n_2 + · · · + 2011y^n_{2011} = a^{n+1}+1$ Jan 11 awarded Student Jan 11 asked Are all metric spaces topological spaces?