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Upper bound on $\sum_{n=1}^\infty q^{(n^2)}$

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#real-analysis #sequences-and-series #power-series
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Prove by induction $\sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}{4}$

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#sequences-and-series #induction
100
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help with an infinite series, hypergeometric function

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#sequences-and-series #hypergeometric-function #q-series
100
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Prove by induction $\sum_{i=1}^n i\cdot 2^{i-1} =(n-1)\cdot 2^n+1$

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#sequences-and-series #induction
292
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Additive basis of order $2$ (II)

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#sequences-and-series #number-theory #elementary-number-theory #additive-combinatorics
1.2k
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Show that if $(x_n)\rightarrow 2$ then $(1/x_n)\rightarrow 1/2$

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#sequences-and-series #limits
8.1k
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Does an alternating sequence converge or diverge or none?

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#sequences-and-series #convergence-divergence
55
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Convergence of the alternating series

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#sequences-and-series #convergence-divergence
65
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A subsequence of the worst-case subsequence

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#real-analysis #sequences-and-series #limits #limsup-and-liminf
381
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An Interesting subsequence problem

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#sequences-and-series #combinatorics #permutations
179
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How to understand a sequence is a function?

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#calculus #sequences-and-series
126
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Coefficient of $x^k$ in ${(1 - e^x)}^{-n}$

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#sequences-and-series #taylor-expansion #exponential-function #binomial-theorem
73
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Find the time complexity of the given code

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#sequences-and-series #logarithms #computer-science
57
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How to show following converges to $1$ uniformly?

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#sequences-and-series #analysis #summation #uniform-convergence
294
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How is $\frac{1}{2n} \leq \sin (\frac{1}{n}) \leq \frac{1}{n} $

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#real-analysis #sequences-and-series #trigonometry

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