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15
492
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Series of $-\sum_{k=1}^{\infty}\frac{(-1)^k}{1+k^2}$

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#sequences-and-series #power-series
74
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Divergence by definition for the sequence $a_{n}=(-1)^n\frac{n}{n+5}$

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#real-analysis #sequences-and-series #convergence-divergence
39
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If we find a Taylor Series for a function and then evaluate were it converges must it represent a power series?

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#sequences-and-series #power-series #taylor-expansion
42
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$\sum_{n=-\infty}^{\infty} \ z_n$ what is mean of this series converge

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#real-analysis #sequences-and-series #analysis
197
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Radius of converge of $\sum_{n = 0}^{\infty}\frac{n}{n^{2}\sqrt{n} + 1}x^{n}$

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#calculus #sequences-and-series #limits #convergence-divergence #power-series
59
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irrationality of $e$ and series

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#real-analysis #sequences-and-series #irrational-numbers
375
Views

Convergence of $1+\frac13-\frac12+\frac15+\frac17-\frac14+\frac19+\frac1{11}-\frac16+\ldots$

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#real-analysis #sequences-and-series
65
Views

Proving a space is not complete by finding an absolutely convergent series

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#sequences-and-series #hilbert-spaces #banach-spaces #complete-spaces #absolute-convergence
40
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Question on the convergence of a sequence if its recurrence relation is given.

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#sequences-and-series #recurrence-relations
156
Views

What is the partial sum of :$\sum_{n=1}^{+\infty}\zeta(n)e^{-n^2}$ and what about it's closed form?

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#sequences-and-series #convergence-divergence #riemann-zeta
147
Views

A conjecture about the asymptotic of the absolute value of $\sum_{k=1}^n\sin\left(N_k\right)$, where $N_k$ is the primorial of order $k$

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#sequences-and-series #asymptotics #analytic-number-theory #trigonometric-series #primorial
95
Views

Order of growth of a recurrence equation

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#sequences-and-series #convergence-divergence
54
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Solving alternate infinite series

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#sequences-and-series #convergence-divergence #prime-numbers
494
Views

Show that if $(A,d)$ is complete then $A$ is closed.

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#real-analysis #sequences-and-series #metric-spaces #cauchy-sequences
481
Views

Basel problem, numerically

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#sequences-and-series #summation #numerical-methods #programming

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