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Find with proof the infimum and supremum of a sequence

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#real-analysis #sequences-and-series
99
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Showing that $\frac 1 {(x+1)^2}=\frac 1 {(x+1)(x+2)}+\frac {1!} {(x+1)(x+2)(x+3)} + \frac {2!} {(x+1)(x+2)(x+3)(x+4)} + \cdots$

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#sequences-and-series
16.4k
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Function which creates the sequence 1, 2, 3, 1, 2, 3, ...

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#sequences-and-series #functions #discrete-mathematics #modular-arithmetic
29
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Study the convergence of the sequence defined by the sum of all modules of $\ z_n$.

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#real-analysis #sequences-and-series #limits #convergence-divergence #limits-without-lhopital
512
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If the sum of any finite terms in a sequnce is less than or equal to epsilon, then prove that the infinite sum is also less than or equal to epsilon.

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#real-analysis #sequences-and-series #infinitesimals
69
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Show that $\ x_n$ is correctly defined if $2^{x_n}+3^{x_n}= n$

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#calculus #real-analysis #sequences-and-series
200
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Explicit summation of a cosine series

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#sequences-and-series #fourier-series #hypergeometric-function
778
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Assuming $\sum n a_n$ converges, does it follow that $\sum a_n$ converge?

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#sequences-and-series #convergence-divergence
111
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Is there any pseudoprime, $p$ such that $p\not\equiv\pm{1\bmod{18}}$?

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#sequences-and-series #prime-numbers #recurrence-relations #primality-test
376
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Optimization of a non smooth function using a smooth approximation.

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#real-analysis #sequences-and-series #optimization #algorithms
79
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Is my proof in calculus correct?

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#calculus #sequences-and-series #proof-verification #proof-writing
260
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Cesaro-Stolz limit

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#real-analysis #sequences-and-series #limits #recurrence-relations
54
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Determine the following limits

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#real-analysis #sequences-and-series #limits
299
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Uniform convergence of power series with decreasing coefficients

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#sequences-and-series #complex-analysis #power-series #holomorphic-functions
2.3k
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Decreasing and bounded below sequence

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#real-analysis #sequences-and-series

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