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Primes in arithmetic progression with the first term and the common difference of minimum values.

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#sequences-and-series #prime-numbers
29
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Why is $a$ an accumulation point in $D=(a,b)$?

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#real-analysis #sequences-and-series
254
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Is it possible to have a closed formula for a sequence 2, 4, 6, 8, ... and the sequence would be equidistributed?

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#sequences-and-series #recreational-mathematics #equidistribution
46
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Understanding Bolzano-Weirstrass theorem for this true/false question

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#real-analysis #sequences-and-series
48
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Proving that series with recursive function $n(n-1)a_n = (n-1)(n-2)a_{n-1} - (n-3)a_{n-2}$

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#real-analysis #sequences-and-series #taylor-expansion
255
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Exact value of a convergent series: $\sum_{n=1}^\infty \frac{1}{n^3+6n^2+8n}$

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#calculus #sequences-and-series
66
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Prove that a sequence related with hypergeometric function is increasing

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#sequences-and-series #hypergeometric-function
150
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Finding Sum of $\frac{1}{4!}+\frac{4!}{8!}+\frac{8!}{12!}+\frac{12!}{16!}+\cdots \cdots \cdots \infty$

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#sequences-and-series
312
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If $a_1 = 3$ and $a_{n+1}=a_n^2-2$, then $\frac{1}{a_1}+\frac{1}{a_1a_2}+\frac{1}{a_1 a_2 a_3}+\cdots = \frac{3-\sqrt{5}}{2}$

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#sequences-and-series #limits
199
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Asymptotics of the sequence defined by $x_{n+1} = x_n + \frac{2}{x_n}$, $x_0=1$

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#sequences-and-series #limits
153
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How to prove that $x_{n+1}=\sqrt[k]{a+x_n}$ is bounded above?

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#real-analysis #sequences-and-series
719
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Give a counter example: $f_n\cdot g_n$ uniformly convergent then $f_n$ or $g_n$ uniformly convergent.

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#real-analysis #sequences-and-series #uniform-convergence
22
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Proving two sequences overlap

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#sequences-and-series #invariance
39
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If the limit of the sum exists, then the limit of each component exists

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#sequences-and-series #limits
97
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$\lim_{n\rightarrow \infty} (a_n+b_n)=0$ $\lim_{n\rightarrow \infty} (b_n-c_n)=0$ imply $\lim_{n\rightarrow \infty} (a_n+c_n)=0$?

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#sequences-and-series #limits

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