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Exchanging order of limits

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#real-analysis #sequences-and-series #limits
107
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Prove: $\sum_{n=1}^\infty a_n$ converges iff $\sum_{n=1}^\infty \int_0^{a_n}g(t) \, dt$ converges

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#calculus #real-analysis #sequences-and-series
1.1k
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Proving the Riesz Representation Theorem for $\ell^p$.

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#real-analysis #sequences-and-series #measure-theory #riesz-representation-theorem
78
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Finite sum where every term is a square root

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#sequences-and-series #summation
196
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How to find the interval of p such that the series is convergent?

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#calculus #sequences-and-series
63
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A problem regarding a sequence in $C[0;1]$

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#sequences-and-series #functional-analysis #convergence-divergence
1.2k
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What is the value of $\sin 1 ^\circ \sin3^\circ\sin5^\circ \sin 7^\circ \sin 9^\circ \cdots \sin 179^\circ $?

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#sequences-and-series #trigonometry
159
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Convergence for sums of independent r.v.'s.

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#sequences-and-series #probability-theory #convergence-divergence #random-variables #borel-cantelli-lemmas
37
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Convergence of a function

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#sequences-and-series
92
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What is the Relationship Between a Sand Pendulum and Infinite Series?

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#calculus #sequences-and-series #harmonic-functions #parametrization
69
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Finding x according to a series

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#calculus #sequences-and-series
75
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Limit of pseudo-series

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#sequences-and-series #limits #uniform-convergence
276
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Prove the coefficients of $\prod_{k=2}^{n+1}(1-x^{a_k})$ are $0$, $1$, or $-1$ where $(a_k)$ are Fibonacci numbers.

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#sequences-and-series #polynomials #fibonacci-numbers
40
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is it true that for every real number x there is a sequence of rationals (of the form m/2^n) that converges to x ??

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#sequences-and-series #rational-numbers
109
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How do I express this proof of absolute convergence as tersely as possible?

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#sequences-and-series #reference-request #proof-writing

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