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Oct
20
comment Rate of convergence of $\left[ \left( \sum\limits_{i=j}^n {2i+1}\right)^{\frac{1}{2}}\right]$
$[\ ]$ is for integer parts, $\{\ \}$ for fractional parts.
Oct
20
answered Rate of convergence of $\left[ \left( \sum\limits_{i=j}^n {2i+1}\right)^{\frac{1}{2}}\right]$
Oct
20
comment Eigenvectors of $\left( \begin{array}{ccc} a & 0 \\ 0 & -b \end{array} \right)$
"Assuming $a\neq 0 \neq b$" Why?
Oct
20
comment Verifying solution of difference equation?
Maybe you can show that $h_x=t_1^x$ solves the difference equation, then that $h_x=t_2^x$ solves it as well, then the full case? What is stopping you?
Oct
20
comment Ladder against a wall.
"In this form" refers to the fact that the sequence of coefficients of the polynomial is symmetric with respect to its midpoint, here (a,b,c,b,a).
Oct
20
revised Prove the inequality$\int_0^{+\infty} {\sin x \over x}dx<\int_0^\pi {\sin x \over x}dx$
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Oct
20
revised Prove the inequality$\int_0^{+\infty} {\sin x \over x}dx<\int_0^\pi {\sin x \over x}dx$
added 1 character in body; edited title
Oct
20
answered Prove the inequality$\int_0^{+\infty} {\sin x \over x}dx<\int_0^\pi {\sin x \over x}dx$
Oct
20
comment The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
@bd1251252 Re the period, note that $\sin((n+12)\pi/6)=\sin((n\pi/6)+2\pi)=\sin(n\pi/6)$. Re the 5, see my answer.
Oct
20
comment How to derive this inequality
Added the argument.
Oct
20
revised How to derive this inequality
added 262 characters in body
Oct
20
comment The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
Alternatively, compute explicitely the first values of the sequence and observe what you get...
Oct
20
comment The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
@bd1251252 My previous comment deals only with the number of distinct values and does not touch on limsup and liminf. If you want to understand where 12 and 5 are coming from, posting cryptic comments is not the best way to proceed. Re 12: what might be the period of the sequence of general term sin(n.pi/6), according to you?
Oct
20
comment The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
The period is 12, a priori this makes for 12 numbers. But amongst these, 5 values are achieved twice and 2 values are achieved only once. Thus 5+2 distinct values.
Oct
20
answered How to derive this inequality
Oct
20
comment The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
Example of what?
Oct
20
revised The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
added 107 characters in body
Oct
20
comment The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
@bd1251252 ?? Know what a periodic sequence is?
Oct
20
comment The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$
@bd1251252 Period 12 and 5 values achieved twice in each period make for 12-5=7 distinct values.
Oct
20
answered The sequence $\sin \left({n\pi}\over 6\right)$ has the superior limit $L=1\dots$