111 reputation
18
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location Istanbul, Turkey
age 26
visits member for 1 year, 8 months
seen Apr 19 at 12:06

Apr
19
accepted How can I show that there are only finitely many solutions for the following system?
Aug
25
comment How can I show that there are only finitely many solutions for the following system?
sorry for the tag and thanks for the hint.
Aug
25
asked How can I show that there are only finitely many solutions for the following system?
Jul
22
awarded  Enthusiast
Jul
15
awarded  Scholar
Jul
15
accepted Does there exist a set in the plane such that topological dimension 2 with empty interior?
Jul
15
accepted How to show that this limit $\lim_{n\rightarrow\infty}\sum_{k=1}^n(\frac{1}{k}-\frac{1}{2^k})$ is divergent?
Jul
15
accepted Find the limit $\displaystyle\lim_{n\rightarrow\infty}{(1+1/n)^{n^2}e^{-n}}$?
Jul
15
accepted How to show that $\sqrt{1+\sqrt{2+\sqrt{3+\cdots+\sqrt{2006}}}}<2$
Jul
15
revised find angle in triangle
added 24 characters in body
Jul
15
awarded  Teacher
Jul
15
answered find angle in triangle
Jul
3
comment How to show that this limit $\lim_{n\rightarrow\infty}\sum_{k=1}^n(\frac{1}{k}-\frac{1}{2^k})$ is divergent?
@julien, thanks.
Jul
3
comment How to show that this limit $\lim_{n\rightarrow\infty}\sum_{k=1}^n(\frac{1}{k}-\frac{1}{2^k})$ is divergent?
So, Is this enough to say this series is divergent?
Jul
3
asked How to show that this limit $\lim_{n\rightarrow\infty}\sum_{k=1}^n(\frac{1}{k}-\frac{1}{2^k})$ is divergent?
Jun
30
awarded  Informed
Jun
30
awarded  Commentator
Jun
28
comment Prove that $\sqrt{7}^{\sqrt{8}}>\sqrt{8}^{\sqrt{7}}$
$\sqrt{7}^{16}>\sqrt{8}^{14}$. So if we take $\frac{1}{2}$ power of both sides, we have $\sqrt{7}^{8}>\sqrt{8}^{7}$. Maybe i am wrong.
Jun
28
comment Prove that $\sqrt{7}^{\sqrt{8}}>\sqrt{8}^{\sqrt{7}}$
It is true that $7^8>8^7$, since $(1+\frac{1}{7})^7<e<7$. Then we have, $\sqrt{7}^8>\sqrt{8}^7$. Does it imply that $\sqrt{7}^\sqrt{8}>\sqrt{8}^\sqrt{7}$.
Jun
17
comment $\frac{c}{1+c}\leq\frac{a}{1+a}+\frac{b}{1+b}$ for $0\leq c\leq a+b$
You can also use the monotone increasing property of $\frac{x}{1+x}$ for proving $\frac{d(x,y)}{1+d(x,y)}$ is a metric.