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Existing $a$ and $b$ that given sequence doesn't contain prime number

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#sequences-and-series #number-theory #modular-arithmetic #recurrence-relations
175
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Does $ \sum_{n=1}^{\infty} (-1)^n\frac{3n-2}{n+1}\frac{1}{n^{1/2}}$ converge?

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#real-analysis #sequences-and-series #convergence-divergence
577
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Given the equation $\sum_{k=11}^{99} \left[x + \frac{k}{100} \right] = 765$ find $[10 \, x]$.

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#linear-algebra #sequences-and-series #polynomials #ceiling-and-floor-functions
113
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Variant of Stieltjes constants

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#sequences-and-series #definite-integrals #fractional-part #stieltjes-constants
64
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Check if $a_n=(n-1)/(n+1)$ is bounded

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#sequences-and-series #upper-lower-bounds
1.2k
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Evaluate the Sum $S=\frac{1}{4}+\frac{1.3}{4.6}+\frac{1.3.5}{4.6.8}+\cdots \infty$

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#sequences-and-series #convergence-divergence #binomial-coefficients #infinite-product
56
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Given $x_1 = a^{1\over k}$ and $x_{n+1} = \left({a\over x_n}\right)^{1\over k}$ prove that $x_n = a^{1-(-k)^{-n} \over k +1}$

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#sequences-and-series #algebra-precalculus
291
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Signed harmonic series containing floor function

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#real-analysis #sequences-and-series #convergence-divergence #ceiling-and-floor-functions
340
Views

Does the series diverge or converge

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#calculus #sequences-and-series
276
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Convergence of $a_1=1,a_2=\sqrt{7},a_3=\sqrt{7\sqrt{7}}, a_4=\sqrt{7\sqrt{7\sqrt{7}}}, \dots$

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#calculus #real-analysis #sequences-and-series #proof-verification
72
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The derivative of $\ln(x)$

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#sequences-and-series #functions #derivatives #logarithms #power-series
38
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Find a sequence $a_f(k)$ so that $\sum_{k=1}^\infty a_f(k) \operatorname{sinc} (\pi k f) = 0$.

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#real-analysis #sequences-and-series
61
Views

Ambiguous or informal ellipses

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#real-analysis #sequences-and-series
253
Views

How to prove convergence of $\sum\limits_{n=1}^\infty \frac{\sqrt a_n}{n^\alpha}$

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#sequences-and-series #convergence-divergence
236
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How to construct a counterexample to $\lim_{n\to\infty} \int_0^1 f_n(x)dx=\int_0^1f(x)dx$

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#real-analysis #integration #sequences-and-series #convergence-divergence

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