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Jul
13
awarded  Yearling
Jul
11
revised IMO 2014 problem 3, first day
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Jul
11
revised IMO 2014 problem 3, first day
added 7 characters in body
Jul
11
answered IMO 2014 problem 3, first day
Jul
2
awarded  Curious
Jul
2
revised Spectral norm of a Hadamard product
added 30 characters in body
Jul
2
asked Spectral norm of a Hadamard product
Jun
20
revised QM-AM-GM-HM proof help
added 274 characters in body
Jun
20
comment QM-AM-GM-HM proof help
@jonnytan999 The way I know to prove this claim, requires taking one derivative, though. Do you need an elementary solution (i.e., without any calculus involved)?
Jun
20
comment QM-AM-GM-HM proof help
@jonnytan999 Yes, as I mentioned particular values of $M(p)$ give you the QM, AM, GM, and HM of the $x_i$s.
Jun
20
comment QM-AM-GM-HM proof help
QM = $M(2)$, AM = $M(1)$, GM = $\lim_{p\to 0} M(p)$, HM = $M(-1)$.
Jun
20
comment QM-AM-GM-HM proof help
@jonnytan999 What notation? I merely defined a function $M(p)$.
Jun
20
answered QM-AM-GM-HM proof help
Jun
16
comment Why am I getting a contradiction?
What have you considered as the "contradiction"? You need the entire epigraph of $f$ to be convex, not just one slice of it.
Jun
14
comment Proving $\forall x\in\mathbb R : \dfrac{e^x + e^{-x}}2 \le e^{\frac{x^2}{2}}$ with Cauchy's MVT
You want to prove $A + B \leq C$, where $B\geq 0$. It's not sufficient to prove $A \leq C$.
Jun
14
comment Proving $\forall x\in\mathbb R : \dfrac{e^x + e^{-x}}2 \le e^{\frac{x^2}{2}}$ with Cauchy's MVT
You are eliminating a non-negative term (i.e., $R_4(x) + S_4(x)$) from the left hand side of the desired inequality. Therefore, what you prove is weaker than what you actually want.
Jun
14
comment Proving $\forall x\in\mathbb R : \dfrac{e^x + e^{-x}}2 \le e^{\frac{x^2}{2}}$ with Cauchy's MVT
$e^{-x} = 1 - x/1! + x^2/2! +\cdots$
Jun
14
comment Proving $\forall x\in\mathbb R : \dfrac{e^x + e^{-x}}2 \le e^{\frac{x^2}{2}}$ with Cauchy's MVT
$e^x = 1 + x/1! + x^2/2! + \cdots$
Jun
11
answered Is this sum $S=\sum_{i,j=1}^n\frac{a_ia_j}{i+j}$ greater than or equal to zero?
Jun
10
reviewed Reject suggested edit on Math for a high school junior?