32,369 reputation
267120
bio website sos440.tistory.com
location Los Angeles, CA
age 26
visits member for 3 years, 4 months
seen 50 mins ago

I am currently a UCLA student, particularly interested in probability theory.

I love mathematics, especially calculating some sort of integrals and summations with inner aesthetic appealing.

Language fluency: (G:green, A:amber, R:red)

  • Korean: Native
  • English: (Reading: G, Listening : A, Speaking : R, Writing : A)
  • Japanese: (Reading : A, Listening : A, Speaking : A, Writing : R)

Aug
19
revised How prove this limit $\left(\frac{1}{2}+\sum_{k=1}^{n-1}(-1)^{\lfloor\frac{mk}{n}\rfloor}\{\frac{mk}{n}\} \right)^n=\frac{1}{\sqrt{e}}$
added 612 characters in body
Aug
19
answered How prove this limit $\left(\frac{1}{2}+\sum_{k=1}^{n-1}(-1)^{\lfloor\frac{mk}{n}\rfloor}\{\frac{mk}{n}\} \right)^n=\frac{1}{\sqrt{e}}$
Aug
19
comment How prove this limit $\left(\frac{1}{2}+\sum_{k=1}^{n-1}(-1)^{\lfloor\frac{mk}{n}\rfloor}\{\frac{mk}{n}\} \right)^n=\frac{1}{\sqrt{e}}$
Observations suggest that the sum is equal to $(n-1)/2n$, but I am still seeking for a proof.
Aug
19
revised Closed form of a complex series sum
added 213 characters in body
Aug
19
answered Closed form of a complex series sum
Aug
17
awarded  Nice Answer
Aug
17
awarded  Revival
Aug
16
comment $a_{n+2} - a_n$ converges to $0$. Prove $\frac {a_{n+1}-a_n}{n}$ converges to $0$
This is an easy application of the Cesaro-Stolz Theorem. Also, there is a same question already posted here.
Aug
14
revised Behavior of $f(z)=\int_0^1\mathrm{e}^{\alpha t^2}\sin(tz)\,dt$ when $\alpha <0$
added 10 characters in body
Aug
14
answered Behavior of $f(z)=\int_0^1\mathrm{e}^{\alpha t^2}\sin(tz)\,dt$ when $\alpha <0$
Aug
14
comment how to find $(I + uv^T)^{-1}$
For $u, v$ with small norm, we can utilize Neumann series to expand the inverse in terms of power series. That yields the desired formula for small $u, v$. Now you can either argue in the opposite direction by claiming and verifying that this formula continues to hold for the other cases, or appeal to the analytic continuation argument.
Aug
14
awarded  Good Answer
Aug
12
revised Does the integral $\int _0^\infty \frac 1{1+(x \cos x)^2}\,dx$ converge?
added 970 characters in body
Aug
12
revised Does the integral $\int _0^\infty \frac 1{1+(x \cos x)^2}\,dx$ converge?
added 970 characters in body
Aug
12
answered Does the integral $\int _0^\infty \frac 1{1+(x \cos x)^2}\,dx$ converge?
Aug
5
awarded  Good Answer
Aug
4
revised Finding the limit of a sequence with an undesirable $\ln k$
New proof added.
Jul
31
answered Solving the power equation $A^X = \frac{(1+X)}{(1-X)}$
Jul
29
awarded  Nice Answer
Jul
22
awarded  Nice Answer