New posts in sequences-and-series

Limit of the geometric sequence

calculus sequences-and-series

convergence of $\sum_{n=1}^{\infty} \frac{e^{-xn\ln x}}{x^2 + n}$ if $x>0$

real-analysis sequences-and-series

Prob. 14, Chap. 3, in Baby Rudin: The arithmetic mean of a complex sequence

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

Is $\frac{1}{2^{2^{0}}}+\frac{1}{2^{2^{1}}}+\frac{1}{2^{2^{2}}}+\frac{1}{2^{2^{3}}}+....$ irrational?

sequences-and-series number-theory rationality-testing

Evaluate $\sum_{k=1}^\infty \frac{k^2}{(k-1)!}$. [duplicate]

calculus sequences-and-series

Is $\prod \limits_{n=2}^{\infty}(1-\frac{1}{n^2})=1$ [duplicate]

real-analysis sequences-and-series infinite-product

Don't understand why this binomial expansion is not valid for x > 1

calculus sequences-and-series convergence-divergence taylor-expansion

For which values of x does the power series converge or diverge?

calculus sequences-and-series convergence-divergence power-series

Evaluating $ \sum\limits_{n=1}^\infty \frac{1}{n^2 2^n} $

calculus real-analysis sequences-and-series algebra-precalculus summation

Is there a convergent, alternating series that fails the AST?

calculus sequences-and-series

$\lim\limits_{n\to\infty} \frac{n}{\sqrt[n]{n!}} =e$ [duplicate]

sequences-and-series analysis limits

How to find explicit formula for two recursions?

sequences-and-series recurrence-relations recursion

Value of this convergent series: $\frac{1}{3!}+\frac2{5!}+\frac3{7!}+\frac{4}{9!}+\cdots$

sequences-and-series convergence-divergence closed-form

For $\sum_{n=1}^\infty z^n \frac{P(n)}{Q(n)}$ where $Q(n)$ and $P(n)$ are polynomials, does di(con)vergence only depends on $z$?

real-analysis sequences-and-series

Prove that there are infinitely many $n$ such that $2018 \mid U_n-1$

sequences-and-series algebra-precalculus number-theory recurrence-relations

Vandermonde's Identity: How to find a closed formula for the given summation [duplicate]

combinatorics sequences-and-series

If there is one perfect square in an arithmetic progression, then there are infinitely many

sequences-and-series number-theory square-numbers arithmetic-progressions

Existence of a sequence that has every element of $\mathbb N$ infinite number of times

sequences-and-series cardinals natural-numbers

Summation over roots of unity

sequences-and-series complex-numbers

Showing that $\displaystyle\limsup_{n\to\infty}x_n=\sup\{\text{cluster points of $\{x_n\}_{n=1}^\infty$}\}$

real-analysis sequences-and-series