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find $\lim_{n→∞}x_n$?..

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#real-analysis #sequences-and-series #convergence-divergence
86
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Sequence and series with specific nth term

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#sequences-and-series
468
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Initial values of Inkeri's primality test for Fermat numbers

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#sequences-and-series #elementary-number-theory #prime-numbers #examples-counterexamples #primality-test
79
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$\sum_n \frac {1 } {\sqrt { n}}-\sqrt{\ln{ \frac{n+1 }{ n}} }$ series convergence

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#calculus #sequences-and-series
251
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Are the sets $\mathbb X=\{0,1,4,15,56,...,x_h,...\} $ and $\mathbb Y=\{0,2,12,70,408,...,y_i,...\}$ (excepting the elements $x_0=y_0=0$) disjunct?

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#sequences-and-series #number-theory #diophantine-equations #pell-type-equations
251
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What are the asymptotics of sums like $\frac16+\frac1{10}+\frac1{14}+\frac1{15}+\frac1{21}+\cdots+\frac1{p_{n-1}p_n}$?

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#real-analysis #sequences-and-series #number-theory #prime-numbers #analytic-number-theory
409
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Dense sets in Hilbert space of square summable sequences?

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#sequences-and-series #hilbert-spaces #lp-spaces #orthonormal
104
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$\sum \exp(-n^{ 1/3})$ series convergence

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#sequences-and-series
1.9k
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Infinite sum converging to 2

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#sequences-and-series #summation
428
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Convergence of $a_{n+2} = \sqrt{a_n} + \sqrt{a_{n+1}}$

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#real-analysis #sequences-and-series #limits #convergence-divergence #cauchy-sequences
60
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Prove that $\sum^\infty_{n\text{ = }m}\big(\frac{a}{e^{n+b}}\big)=\frac{a\,e^{1-\,b\,-\,m}}{e-1}$

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#calculus #real-analysis #sequences-and-series #convergence-divergence
78
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A conjecture on bounded complex partial sums

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#sequences-and-series #complex-analysis #power-series #conjectures #geometric-series
1.9k
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Express the sequence $\{x_n\}$ where $x_n = 2x_{n-1} + 3x_{n-2}$ in terms of ${x_0, x_1, n}$

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#sequences-and-series #summation #recurrence-relations
61
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How to find the sum of a geometric series for which $a_4 =-80$, $a_7=640$, and $n=12$

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#sequences-and-series #geometric-series
144
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Ordinary generating function for $\mu^2(x)$

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#sequences-and-series #generating-functions #mobius-function

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