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15
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Infinite series with finite sum

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#sequences-and-series #paradoxes
249
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Convergence of the series $\sum\limits_{k=1}^{\infty}\left(\sin\frac{1}{k}-\arctan\frac{1}{k}\right)$

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#sequences-and-series
66
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Sequence and two limits to calculate

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#real-analysis #sequences-and-series
117
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Divergence of $\sum_{n=1}^\infty\frac{\mu(n)}{\sqrt{n}}\cos\left(n^2 \pi \gamma\right)$, where $\gamma$ is the Euler-Mascheroni constant

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#real-analysis #sequences-and-series #convergence-divergence #mobius-function #euler-mascheroni-constant
46
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Any series which increases extremely slowly and whose lower bound is $\log^{\circ k}(n+1)$?

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#sequences-and-series #summation #logarithms #divergent-series
3.2k
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Convergence of $\sum (-1)^n \sin^2(n)/n$

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#calculus #sequences-and-series #convergence-divergence
85
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Simplifying Inequality

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#linear-algebra #sequences-and-series #inequality #problem-solving #cauchy-schwarz-inequality
34
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Find relation between these two subsequences

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#sequences-and-series #limits #convergence-divergence
3.8k
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When you inscribe a triangle in a circle in a triangle in a circle in a triangle ...

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#sequences-and-series #general-topology #geometry #euclidean-geometry #recreational-mathematics
657
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Find a pattern and prove it by mathematical induction:

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#sequences-and-series #summation #induction #fibonacci-numbers #arithmetic-progressions
542
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Determine if a sequence is Cauchy

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#calculus #real-analysis #sequences-and-series #cauchy-sequences
34
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How would I write this as a recursive formula?

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#sequences-and-series
220
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For what value of $p$ would the series $\sum_{n=2}^\infty \frac{1}{n^p\ln(n)}$ converge?

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#sequences-and-series #limits #convergence-divergence
112
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Evaluate $\int_0^\infty\sum_{n=0}^\infty\frac{(-1)^n}{(n!)^t}\,dt$

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#calculus #sequences-and-series #improper-integrals
292
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If $a,b,c$ are in arithmetic progression, prove that...

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#sequences-and-series #trigonometry #fractions #arithmetic-progressions

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