New posts in sequences-and-series

Compute the value of the integral $\int_1^{\infty} \lfloor x^2 \rfloor e^{-x} \ \mathrm d x $

calculus integration sequences-and-series definite-integrals

How to prove a property regarding periodicities of points in the Mandelbrot set?

sequences-and-series complex-analysis inequality fractals

What are the rules for convergence for 2 series that are added/subtracted/multiplied/divided?

sequences-and-series convergence-divergence divergent-series

How to prove $\sum_{k=1}^n \cos(\frac{2 \pi k}{n}) = 0$ for any n>1? [duplicate]

sequences-and-series complex-analysis trigonometry complex-numbers trigonometric-series

Bounded sequence in Hilbert space contains weak convergent subsequence

sequences-and-series functional-analysis hilbert-spaces weak-convergence

Double summation $\sum_{m,n=1\, m\neq n}^\infty{\frac{m^2+n^2}{mn(m^2-n^2)^2}}$

sequences-and-series summation

How prove $a_{n}=1!+2!+\cdots+n!$ contains infinitely many prime factors

sequences-and-series number-theory

Strategies For Summing Harmonic Numbers

calculus sequences-and-series harmonic-numbers

Why is the Cauchy product of two convergent (but not absolutely) series either convergent or indeterminate (but does not converge to infinity)?

calculus real-analysis sequences-and-series

Why is $\lim_{x\to 1}\sqrt{1-x}\sum_{n=0}^\infty x^{n^2}=\sqrt{\pi}/2\,\,$? [duplicate]

calculus sequences-and-series limits

An alternative proof for sum of alternating series evaluates to $\frac{\pi}{4}\sec\left(\frac{a\pi}{4}\right)$

calculus real-analysis sequences-and-series alternative-proof

Infinite series for the arctangent from the tangent of half-angle formula

sequences-and-series trigonometry math-history

Does there exist a closed form for $L_k$ for any $k>3$?

sequences-and-series closed-form harmonic-numbers

Number of apples on the tree after n days?

sequences-and-series combinatorics algebra-precalculus

Limit of the quotient of sums of recurrent relations

real-analysis calculus sequences-and-series limits recurrence-relations

Proof of a theorem of Cauchy's on the convergence of an infinite product

real-analysis sequences-and-series convergence-divergence infinite-product

Evaluate $\lim_{n \to \infty} n^3 \left(\int_0^{\pi}\cosh(2\cos(x)) dx - \pi\sum_{k=0}^n \frac{1}{(k!)^2} \right)$

sequences-and-series integration limits

Does this sequence always give a square number?

sequences-and-series

Find $\sum_{n=1}^{\infty}\int_0^{\frac{1}{\sqrt{n}}}\frac{2x^2}{1+x^4}dx$

real-analysis integration sequences-and-series

Weird limit $\lim \limits_{n\mathop\to\infty}\frac{1}{e^n}\sum \limits_{k\mathop=0}^n\frac{n^k}{k!} $ [duplicate]

sequences-and-series limits