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Application of AM-GM Inequality

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#sequences-and-series #inequality
340
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Solving a recursive formula $a_0=2, a_n=n+\sum_{i=2}^{n-1}a_i$ (Thabit numbers)

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#sequences-and-series #number-theory #recursion
116
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Does the fact that $\lim\limits_{n\to\infty} |f(n)/f(n-1)| = 1$ imply that $\lim\limits_{n\to\infty} f(n)$ exists?

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#calculus #sequences-and-series #limits #ratio
75
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$a_k = \lim\limits_{n\to \infty} \sum\limits_{m=1}^{m=kn} \frac{1}{n} e^{\frac{-m^2}{2n^2}}$

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#sequences-and-series #limits
86
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Proving the uniform convergence of $f_n$

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#real-analysis #sequences-and-series #convergence-divergence #uniform-convergence
946
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Evaluate $\sum\limits_{r=1}^{50}\left[\frac{1}{49+r} - \frac{1}{2r(2r-1)}\right]$

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#sequences-and-series #summation
113
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Existence of infinite product measure (part of proof)

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#sequences-and-series #probability-theory #measure-theory
79
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Why does the infinite iteration of $f(x)={a\over x}+1$ approach ${\sqrt{4a+1}+1\over 2}$?

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#sequences-and-series #limits #dynamical-systems
93
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prove the divergence

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#sequences-and-series
46
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Sequence question problem

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#sequences-and-series
1.5k
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How can I calculate the mean number of attempts needed for success?

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#probability #sequences-and-series #statistics
135
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Rudin definition of Eulers constant e

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#real-analysis #sequences-and-series
94
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Convergence of Sequence of arithmetic mean

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#real-analysis #sequences-and-series #limits
3k
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Fourier series piecewise function

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#integration #sequences-and-series #definite-integrals #fourier-series #trigonometric-integrals
172
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Reducing double limit to single limit

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#sequences-and-series #limits

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