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Evaluate the expression $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\cdots}}}$

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#sequences-and-series #functions #recurrence-relations
115
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how can I prove it is a convergent sequence and how can I calculate its limit

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#calculus #real-analysis #sequences-and-series #recurrence-relations
59
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Proving convergence of a sequence given by $a_{n+1}=A+Ba_n^3$

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#sequences-and-series #convergence-divergence #recurrence-relations
119
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Solving system of equations with summation

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#sequences-and-series #summation #recurrence-relations #systems-of-equations
60
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Prove that a polynomial of this form has a real root of this form.

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#reference-request #polynomials #recurrence-relations #roots
300
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How to solve this nonlinear functional recurrence

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#recurrence-relations #generating-functions #functional-equations
30
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Boundary difference equation, monotonicity of the solution properties.

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#calculus #recurrence-relations #finite-differences
2.5k
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How to find the limit of the sequence $x_n =\frac{1}{2}[x_{n-1}+x_{n-2}]$, if $x_0=0$ and $x_1=1$?

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#sequences-and-series #analysis #convergence-divergence #recurrence-relations #monotone-functions
214
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Not understanding the recurrence formula of n nodes with a height h in an AVL tree to show $2 \log n \geq h$

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#recurrence-relations
47
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How to solve the recurrence

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#recurrence-relations
790
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Solving linear recurrences with repertoire method

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#recurrence-relations
42
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Given that $0<a<b$, $a_0=a$, and $b_0=b$, Show that $a_{n+1}=\sqrt{a_nb_n}$ is always increasing and $b_{n+1}=\frac12(a_n+b_n)$ is decreasing

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#sequences-and-series #recurrence-relations
172
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Limit of complex sequence.

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#complex-analysis #limits #recurrence-relations
100
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Discrete mathematics puzzle

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#discrete-mathematics #recurrence-relations
139
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Does $\{x_n\}$ converge , $x_{n+1}=\frac{2}{3}x_n+ \frac{1}{x_n^2}$

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#real-analysis #sequences-and-series #recurrence-relations

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