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Does $\lim a_n$ exist?

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#real-analysis #sequences-and-series #limits
77
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On the equation $\varphi(2+\varphi(x))=2^{y-1}$, where $\varphi(n)$ denotes the Euler's totient function

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#sequences-and-series #elementary-number-theory #reference-request #totient-function #fermat-numbers
123
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Closed form of $u_n$ with $u_{0} =1$ and $u_n=\frac{1}{3}u_{n-1}-1$?

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#sequences-and-series #recurrence-relations #closed-form
88
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Checking of convergence of a given sequence.

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#real-analysis #sequences-and-series #convergence-divergence
76
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Problem in finding the value of this limit

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#sequences-and-series #limits #definite-integrals #summation
236
Views

Computing $\int \sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{x\cdots}}}} \,\mathrm{d}x$

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#sequences-and-series #definite-integrals
37
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Limit of $\lim_{n\to \infty}\frac{1}{n^{1/2}}\sum_{k=0}^n(\frac{1}{2^{1/2}}(1+i))^k$

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#calculus #sequences-and-series #analysis #limits
119
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Prove that, even if a sequence isn't monotonic, it still converges and has limit.

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#real-analysis #sequences-and-series #limits
77
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find closed form for recurrence relation using generating function. terminate exercise

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#sequences-and-series #recurrence-relations #generating-functions
165
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Evaluate $\lim_{ n \to \infty} \sum_{r=2n+1}^{3n} \frac{n}{r^2-n^2}$

Published on
#integration #sequences-and-series #algebra-precalculus #definite-integrals #summation
206
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$a_n $ is a positive integer for any $n\in \mathbb {N} $.

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#sequences-and-series #induction #recurrence-relations
321
Views

Convergence of series ${\sum_{n >= 1} \sqrt{n}\ln(\cosh(1/n))}$

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#real-analysis #sequences-and-series
17
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Rate of convergence of a sequence in $\mathbb{R}^n$

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#sequences-and-series #convergence-divergence
121
Views

How does one prove $\sum_{n=0}^\infty \frac{(-1)^n}{(n+1)(n+2)} = 2 \log 2 -1$?

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#real-analysis #sequences-and-series
399
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Infinite sum of falling factorial quotients.

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#sequences-and-series

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