New posts in real-analysis

Confusion on the proof of the Divergence Test

real-analysis calculus sequences-and-series

$L^2\cap C^\infty$ Hodge/Helmholtz decomposition on $\Bbb R^n$

real-analysis partial-differential-equations fluid-dynamics

Infinite Series $\sum_{m=0}^\infty\sum_{n=0}^\infty\frac{m!\:n!}{(m+n+2)!}$

calculus real-analysis sequences-and-series binomial-coefficients closed-form

Need a hint: show that a subset $E \subset \mathbb{R}$ with no limit points is at most countable.

What does a well ordering of $\mathbb{R}$ look like? [duplicate]

real-analysis order-theory axiom-of-choice

What are the limit points of $\tan(\mathbb{N})$ in $\mathbb{R}$?

real-analysis general-topology

Does this double series converge?

real-analysis combinatorics sequences-and-series summation

Triangle inequality applied to subtraction?

real-analysis inequality

Infinite Series $\sum\limits_{n=1}^{\infty}\frac{(m-1)^n-1}{m^n}\zeta(n+1)$

real-analysis sequences-and-series complex-analysis closed-form

If $A$ and $B$ are sets of real numbers, then $(A \cup B)^{\circ} \supseteq A^ {\circ}\cup B^{\circ}$

real-analysis general-topology proof-verification

Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.

real-analysis continuity

Prove that $2^n\alpha-[2^n\alpha]$ is dense in [0,1]

Is there a closed a form for $\sum_{n=1}^\infty\frac{(-1)^{n-1}H_{an}}{n}\,?$

real-analysis integration complex-analysis closed-form harmonic-numbers

Find $\sum_{n=1}^{\infty}$ $\frac{n^{2}}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\left(n+4\right)}$

real-analysis sequences-and-series limits reference-request convergence-divergence

Algebraic Basis vs Hilbert basis

linear-algebra real-analysis

Prove that the unit open ball in $\mathbb{R}^2$ cannot be expressed as a countable disjoint union of open rectangles.

real-analysis general-topology

How to decide about the convergence of $\sum(n\log n\log\log n)^{-1}$?

calculus real-analysis sequences-and-series analysis convergence-divergence

Show the sequence converges to M

real-analysis integration sequences-and-series analysis

Fourier Transform of $\ln(f(t))$

real-analysis functional-analysis fourier-analysis

How to evaluate $ \sum\limits_{n=1}^{\infty} \left( \frac{H_{n}}{(n+1)^2.2^n} \right)$

calculus real-analysis sequences-and-series algebra-precalculus harmonic-numbers