Reputation
8,990
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
5 15 49
Newest
 Good Answer
Impact
~65k people reached

18h
revised Convergence: infinite series
edited tags
18h
answered Convergence: infinite series
19h
comment Convergence: infinite series
Intuitive hint: the inequality means that if $b_n$ decreases, then $a_n$ decreases more, and if $b_n$ increases, $a_n$ increases less. So, apart form the first term, you should expect that the finite sums of $a_n$ are less than the finite sums of $b_n$. You can factor out the first terms without changing the successive quotients, to make this more precise.
19h
revised Is $\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)$ always?
edited tags
19h
comment Evaluation of $ \int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx $
Nice answer, and nice LaTeX lesson ;-)
20h
revised Evaluation of $ \int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx $
added 692 characters in body
20h
revised Evaluation of $ \int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx $
added 692 characters in body
20h
answered Evaluation of $ \int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx $
20h
comment How do I find the determinants of $3A, -A, A^2, A^{-1}$, where A is an $4\times 4$ matrix and $\det(A) = \frac{1}{3}$?
For the (2), you can also use the fact that it's a multilinear form.
21h
revised Textbook +reference book in complex analysis
added 11 characters in body
23h
comment How prove that $\frac{1}{\sin^2\frac{\pi}{2n}}+\frac{1}{\sin^2\frac{2\pi}{2n}}+\cdots+\frac{1}{\sin^2\frac{(n-1)\pi}{2n}} =\frac{2}{3}(n-1)(n+1)$
This will be helpful: math.stackexchange.com/questions/544228/…
1d
revised A math contest question related to Ramsey numbers
edited tags
1d
comment show that $(1 +\sin{A}) + \cos^2{A} = 2(1 + \sin{A})$?
Wrong. Try substituting $A =\pi/2$.
1d
comment Finding pattern
@Chou But then no answer leaves this property true, since the only primes are $2,3,11$, and they are all divisible by $5$.
1d
revised how to prove that a relation is antisymmetric?
added 7 characters in body
1d
revised how to prove that a relation is antisymmetric?
added 22 characters in body
1d
revised how to prove that a relation is antisymmetric?
added 6 characters in body
1d
answered how to prove that a relation is antisymmetric?
1d
reviewed Reject To prove ($A\cup B$) $\cap C$ = $(A \cup C) \cap (B \cup C)$
1d
reviewed Close basic word problem!