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Infinity_hunter
  • Member for 3 years, 7 months
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  • Hilbert spaces
9 votes
Accepted

Factoring $2$ from $3^x + 1$

7 votes
Accepted

Proving the Alternate Series Test

6 votes

What are some examples of infinite dimensional vector spaces?

6 votes
Accepted

Find a commutative ring $R$ such that for a, b in R such that $a\neq b$ $a^n=b^n$ and $a^m=b^m$ where n and m are relatively prime.

5 votes
Accepted

Finding the limit as $x$ tends to $0^{+}$

5 votes

Let $G$ be a multiplicative group of all positive real numbers and $\Bbb R$ be the additive group of all real numbers. Is $G\le\Bbb R$?

5 votes
Accepted

Find the nth derivative of $\cos(x^3)$

5 votes

$\arctan(\frac{x+1}{x-1})$ to power series

5 votes

Let $m, n ∈ \mathbb{N}$ such that $2m^{2} + m = 2n^{2} + n$ , then prove that $m-n$ is a perfect square .

5 votes
Accepted

Prove that $\iint_{\left[ 0,1 \right] \times \left[ 0,1 \right]}{\frac{f\left( x \right)}{f\left( y \right)}\text{d}x\text{d}y\ge 1}$

5 votes
Accepted

Points of discontinuity of $\left[\frac{f(x)}3\right], f(x)=\lim_{n\to\infty}\ln(\sqrt{e^{\cos x}\sqrt{e^{3\cos x}...\sqrt{e^{(2n+1)\cos x}}}})$

5 votes
Accepted

Limitations of algebra

4 votes
Accepted

Summation e^(i/n)

4 votes
Accepted

Approximation method for the Basel Problem.

4 votes

Euler totient function sum of divisors. Theorem 2.2 Apostol

4 votes
Accepted

Splitting field of $x^4 + 1$ over $Q$

4 votes
Accepted

Evaluate $\int \cfrac{150u^3}{e^{\pi u}-1}du$

4 votes

If $\alpha^{2}$ is algebraic over F, then show that $\alpha$ is algebraic over F.

4 votes

Partial sums of $\sum_{n = 1}^{\infty}\frac{1}{n(n + 1)(n + 2)}$

4 votes

Show that $(\mathbb{R}^*, \cdot)$ is not cyclic.

4 votes

Linear algebra book for early phd student

3 votes

Factoring $\frac{n(n+1)}2x^2-x-2$ for $n\in\mathbb Z$

3 votes
Accepted

Proving formula about the least number $n$ such that $a|n$ and $b|(n+1)$, $a,b$ coprime.

3 votes

Is there an angle $\alpha$ that makes both $\cos \alpha$ and $\sin\alpha$ rational?

3 votes
Accepted

Showing that $E(X)=\sum^{\infty}_{n=1}P(X\geq n)$

3 votes
Accepted

If $f(x+y)=f(x)f(y) \ \forall x,y \in \mathbb{R}$ and $f(x)$ is differentiable everywhere. Find f(x).

3 votes

Simple way to compute the finite sum $\sum\limits_{k=1}^{n-1}k\cdot x^k$

3 votes
Accepted

Doubt regarding closed form of $\sum_{k=1}^{n}\text{exp}\left(k\left(\frac{2\pi i}{n}\right)\right)$

3 votes
Accepted

Simplifying $\frac{\zeta'(s)}{\zeta(s)}$

3 votes

Theorem 3.2 of Apostol confusion!!

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