New posts in sequences-and-series

$\lim x_n^{x_n}=4$ prove that $\lim x_n=2$ [duplicate]

calculus sequences-and-series proof-verification

All terms of this sequence are equal to 1: $x_{n+1}= \frac{nx_{n}^2+1}{n+1}$

sequences-and-series elementary-number-theory reference-request recurrence-relations

Show that if $\sum_{n=0}^{\infty}a_n^k=\sum_{n=0}^{\infty}b_n^k$ for all $k\in \Bbb N^*$ then $(a_n) = (b_n)$

sequences-and-series summability-theory

Which positive continuous functions satisfy $F(x) = F(e^x)-F(e^{-x})$ for $x\geq 0$?

sequences-and-series stochastic-processes taylor-expansion functional-equations

Can a composite number $3\cdot 2^n + 1$ divide a Fermat number $2^{2^m}+1$?

sequences-and-series elementary-number-theory divisibility fermat-numbers

Number of Unique Sequences with Circular Shifts

sequences-and-series combinatorics algebra-precalculus combinations binary

Is there a name for the closed form of $\sum_{n=0}^{\infty} \frac{1}{1+ a^n}$?

sequences-and-series special-functions closed-form

Compute this integral

calculus real-analysis integration sequences-and-series definite-integrals

What is the sum $\sum_{k=0}^{n}k^2\binom{n}{k}$? [duplicate]

sequences-and-series binomial-coefficients

Sum of special series: $1/(1\cdot2) + 1/(2\cdot3 )+ 1/(3\cdot4)+\cdots$

sequences-and-series

How to calculate the limit of $\frac{a_n}{n^2}$ for the sequence $a_{n+1}=a_n+\frac{2 a_{n-1}}{n+1}$?

sequences-and-series limits

Prove $\sum_{n=0}^\infty(-1)^n(\overline{H}_n-\ln2)^2=\frac{\pi^2}{24}$

calculus integration sequences-and-series alternative-proof harmonic-numbers

Interchanging Summation and Integral

calculus real-analysis integration sequences-and-series analysis

if $|a|<1$ so $\lim_{n\to \infty}na^n=0$.

sequences-and-series limits

Finding closed form for $1^3+3^3+5^3+...+n^3$

sequences-and-series

Convergence of $\sum_{n=1}^{\infty}\frac{1}{3^n\ \sin(n)}$

real-analysis sequences-and-series

An interesting series $\sum_{n=2}^{\infty} \sum_{k=0}^{\infty} \frac{1}{(2k+3)^n-1}$

calculus real-analysis sequences-and-series

Show $\sum \frac{1}{p}(-1)^{(p-1)/2}$ converges

sequences-and-series analysis prime-numbers

Are there certain conditions that $a_n$ must meet in order for this series to converge?

sequences-and-series convergence-divergence

Finding a closed form expression for $\sum_{i=1}^{n-1}\csc{\frac{i\pi}{n}}$

sequences-and-series trigonometry summation