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14h
comment Let $\{x_n\}$ be a sequence of positive reals, show that $\limsup\sqrt[n] {x_n}\leq\limsup \frac{x_{n+1}}{x_n}$.
err... actually why is after finite humber of terms, everything is less than $\limsup{x_{n+1}}/{x_n}+\epsilon$? the $x_1/x_2$ can be arbitrarily large....
1d
comment Let $\{x_n\}$ be a sequence of positive reals, show that $\limsup\sqrt[n] {x_n}\leq\limsup \frac{x_{n+1}}{x_n}$.
Ahhhh I didn't know to get rid of the $x_1$ so I failed. Now I get it, thanks.
1d
comment Let $\{x_n\}$ be a sequence of positive reals, show that $\limsup\sqrt[n] {x_n}\leq\limsup \frac{x_{n+1}}{x_n}$.
@ dan: is RHS of your equation missing a $x_1$?
1d
asked Let $\{x_n\}$ be a sequence of positive reals, show that $\limsup\sqrt[n] {x_n}\leq\limsup \frac{x_{n+1}}{x_n}$.
May
4
awarded  Notable Question
May
1
accepted Show that $D(A,B):=\inf\{r:A\subseteq N_r(B) \text{and}B\subseteq N_r(A)\}$ is a metric on bounded closed subsets of $X$.
May
1
asked Show that $D(A,B):=\inf\{r:A\subseteq N_r(B) \text{and}B\subseteq N_r(A)\}$ is a metric on bounded closed subsets of $X$.
Mar
24
comment how to factor $x^4+2x^3+4x^2+3x+2$
I remembered I observed the tiny bit of symmetry of the terms.
Mar
7
awarded  Popular Question
Feb
27
awarded  Yearling
Jan
5
awarded  Nice Answer
Jan
4
accepted Computation of a indefinite integral: $ \int \frac {dx} {x^n-1}$
Jan
4
accepted How to better define $f(n)=\begin{cases} 1,&n\text{ even} \\ 0, &n\text{ odd}\end{cases}$?
Jan
3
comment Computation of a indefinite integral: $ \int \frac {dx} {x^n-1}$
No need to add 1/(z+1) if z even , right?
Jan
3
asked How to better define $f(n)=\begin{cases} 1,&n\text{ even} \\ 0, &n\text{ odd}\end{cases}$?
Jan
2
comment Computation of a indefinite integral: $ \int \frac {dx} {x^n-1}$
There isn't any, it's indefinite...
Jan
2
revised Computation of a indefinite integral: $ \int \frac {dx} {x^n-1}$
deleted 2 characters in body
Jan
2
comment Computation of a indefinite integral: $ \int \frac {dx} {x^n-1}$
Thanks, corrected.
Jan
2
asked Computation of a indefinite integral: $ \int \frac {dx} {x^n-1}$
Dec
21
accepted Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.