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Deriving values for the Riemann zeta function on even natural numbers through recurrence

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#sequences-and-series #recurrence-relations #riemann-zeta
567
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What is the value of $\sqrt{1+ \sqrt[3]{1+\sqrt[4]{1+ \sqrt[5]{1+ \cdots }}}}$?

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#sequences-and-series #limits #nested-radicals
2.2k
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What is the meaning of the phrase "Power series expansion about $x = 0$"?

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#sequences-and-series #taylor-expansion
71
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Integral $\int_0^1 \frac{ sin(\pi x)}{x+n }dx$

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#sequences-and-series #analysis
348
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Understanding an aplication of Faà di Bruno's formula

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#sequences-and-series #derivatives #power-series #taylor-expansion
104
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Construct $(y_n)$ such that $x_n \leq y_n \leq 2y_{f(n)}$ where $f:\mathbb{N}_{\geq 0} \to \mathbb{N}_{\geq 1}$ is strictly increasing

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#calculus #real-analysis #sequences-and-series #functions #convergence-divergence
36
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Sums of different infinite series equal the same thing?

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#sequences-and-series #summation
33
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Series convergence for every real number

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#real-analysis #sequences-and-series #limits #convergence-divergence
54
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Limit of the following term

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#calculus #sequences-and-series #limits #derivatives #infinity
1.9k
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solve for x within a summation equation

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#sequences-and-series #trigonometry #trigonometric-series
61
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The asymptotic behaviour of an arithmetic function related to the $K$-function

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#sequences-and-series #prime-numbers #asymptotics #analytic-number-theory
139
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Does the series $\sum^{\infty}_{n=1}\frac{2n^{5}+13n^{3}}{n^{\frac{1}{n}}(n^6-n^2+7)}$ converge or diverge? Justify.

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#real-analysis #sequences-and-series
81
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How can one show that this is positive?

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#sequences-and-series #exponential-sum
60
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Where does the choice of $n$ come from in this proof of $\inf \left\{\exp((-1)^nn)\right\} = 0$?

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#real-analysis #sequences-and-series #supremum-and-infimum
50
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Is this sequence a integer?

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#sequences-and-series #number-theory #proof-verification

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