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Is $\sin (1+ \frac{x}{n})$ decreasing function

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#real-analysis #sequences-and-series #functions #trigonometry
189
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Question about sequences.

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#sequences-and-series #discrete-mathematics #definition
53
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Finiteness of the supremum of a function

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#real-analysis #sequences-and-series
93
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Prove that $\sum_{k\ge 1}\frac{kg(x^2)}{1+k^3[g(x^2)]^2}$ does not converge uniformly on the real line

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#calculus #real-analysis #sequences-and-series #convergence-divergence #uniform-convergence
95
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Generating equation for Diophantine equation

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#sequences-and-series #diophantine-equations
1.1k
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What does $\lim\sup {a_n}$ or $\lim\inf {a_n}$ mean?

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#real-analysis #sequences-and-series
230
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Convergence of angle between vectors?

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#real-analysis #sequences-and-series #proof-verification
38
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Finding a function within a convergent sum involving the harmonic numbers so that the equality holds

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#real-analysis #sequences-and-series
60
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What is the summation of squared deviation wrt $\ell_2$-norm from vector mean in terms of individual deferences?

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#sequences-and-series #machine-learning
1.9k
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OEIS database download

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#sequences-and-series #oeis
138
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Calculating $\sum_{n=1}^{\infty} r^n \cos n\theta$

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#calculus #sequences-and-series
2.3k
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Every sequence has a weakly convergent subsequence with limit

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#sequences-and-series #functional-analysis #compactness #reflexive-space
535
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General P-series rule

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#sequences-and-series #summation #pi
115
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A convergent sum of a divergent and convergent sequence?

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#real-analysis #sequences-and-series #limits #proof-verification #convergence-divergence
839
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Does $\sum_{n=1}^{\infty}\arctan(\frac{1}{n^2})$ converge?

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#calculus #sequences-and-series #convergence-divergence #divergent-series

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