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Show that $\lim_{x \to 1} \sum_{n=1}^{\infty}\frac{n x^2}{n^3 + x^2}= \sum_{n=1}^{\infty} \frac{n}{n^3 +1}$.

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#real-analysis #uniform-convergence
369
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Show that $f_n$ converges uniformly to $f=0$

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#real-analysis #uniform-convergence #alternative-proof #sequence-of-function
182
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$C^\infty$ $f_n$ converge pointwise $\implies$ f is $C^\infty$

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#real-analysis #derivatives #uniform-convergence #sequence-of-function #pointwise-convergence
48
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Question on pointwise convergence of Sequence of functions

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#real-analysis #continuity #uniform-convergence #sequence-of-function #pointwise-convergence
142
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On uniform convergence in normal families of functions

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#complex-analysis #uniform-convergence #normal-families
54
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Uniform convergence sequence of positive reals

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#real-analysis #uniform-convergence #sequence-of-function
3.7k
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Uniform convergence implies pointwise convergence

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#real-analysis #sequences-and-series #proof-writing #solution-verification #uniform-convergence
409
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$f_n(x) = \log(1 + n^3 x^2)/n^2$ (uniform converge)

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#real-analysis #uniform-convergence #sequence-of-function
1.2k
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Pointwise and uniform convergence of $f_n(x)=xe^{-nx}$

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#analysis #convergence-divergence #uniform-convergence #pointwise-convergence
60
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Is sequential criterion of continuity holds for Sequence of continuous functions?

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#real-analysis #convergence-divergence #uniform-convergence #sequence-of-function
83
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Check the pointwise and the uniform convergence of $(f_n)_n:D\rightarrow \mathbb{R}$

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#real-analysis #convergence-divergence #solution-verification #uniform-convergence #pointwise-convergence
104
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Pointwise and uniform convergence of sum

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#analysis #convergence-divergence #uniform-convergence #pointwise-convergence
94
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Why does this function series converges uniformly?

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#sequences-and-series #power-series #uniform-convergence
155
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The convergence of an integral, dependant on a parameter

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#real-analysis #improper-integrals #uniform-convergence
45
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A "Fourier Series" for $\sin$?

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#real-analysis #fourier-series #uniform-convergence

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