New posts in sequences-and-series

Does $\sum_{k=0}^{\infty}\sin\left(\frac{\pi x}{2^k}\right)$ have a simple form with interesting properties?

sequences-and-series summation trigonometric-series

Find the 8th derivative of the function $h(x) = xe^x $using sequences

sequences-and-series derivatives taylor-expansion

Is the sequence defined by the recurrence $ a _ { n + 2 } = \frac 1 { a _ { n + 1 } } + \frac 1 { a _ n } $ convergent? [duplicate]

real-analysis sequences-and-series limits convergence-divergence recurrence-relations

Calculating $\sqrt{-1}$

sequences-and-series number-theory quadratic-residues elementary-functions

Closed form solution for the zeros of an infinite sum

sequences-and-series roots closed-form

A theorem about Cesàro mean, related to Stolz-Cesàro theorem

calculus real-analysis sequences-and-series reference-request

Kummer's test - Calculus, Apostol, 10.16 #15.

sequences-and-series convergence-divergence divergent-series

Why is the ratio test for $L=1$ inconclusive?

sequences-and-series intuition limits convergence-divergence

Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

sequences-and-series limits trigonometry recurrence-relations pattern-recognition

Finding the sum $\sum\limits_{n=1,n\neq m^2}^{1000}\left[\frac{1}{\{\sqrt{n}\}}\right]$,

sequences-and-series

Sum of cosines of primes

sequences-and-series prime-numbers convergence-divergence

Prove that $a_n=(-1)^n$ does not converge

sequences-and-series limits solution-verification

Suppose $a_n \ge 0$ for all n and that $\sum_{n=1}^{\infty} (a_n)^2$ converges, does the $\sum_{n=1}^{\infty} a_n$ also converge?

calculus sequences-and-series integer-sequences

Proving a number defined by a sequence is a square number

sequences-and-series elementary-number-theory exponentiation problem-solving

How to find finite trigonometric products [closed]

calculus sequences-and-series trigonometry products

Closed form for $a_{n+1} = (a_n)^2+\frac{1}{4}$

sequences-and-series recurrence-relations

Formal (series/sum/derivative...)

sequences-and-series derivatives power-series

Sums in $\mathbb N^3$

real-analysis sequences-and-series convergence-divergence

A Detailed explanation for Archimedes area of parabolic segment by exhaustion proof ? Needed

calculus sequences-and-series algebra-precalculus proof-explanation area

why $\frac{f_n}{f_kf_{n-k}}$ is an integer for this sequence

sequences-and-series number-theory fibonacci-numbers algebraic-combinatorics