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Computing the series$\sum\limits_{k=1}^{\infty}{\frac{3^{k-1}+(2i)^k}{5^k}} $

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#real-analysis #sequences-and-series #analysis #limits #convergence-divergence
448
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For which values of $x$ does the following series converge?

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#real-analysis #sequences-and-series
112
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Find the sum of infinite series

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#real-analysis #sequences-and-series #definite-integrals #summation #power-series
68
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Limit of $((1+z_n)^{1/z_n})^{\log n}$ for sequence $z_n\to 0$.

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#sequences-and-series
40
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Are one-dimensional maps still called the same if they involve multiple functions instead of one recurrent function?

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#sequences-and-series #ordinary-differential-equations #dimensional-analysis
6.5k
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Summation of Squares of Fibonacci numbers

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#sequences-and-series #proof-verification #induction
154
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Convergence of a series involving $\sin(n)^n$

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#real-analysis #sequences-and-series #trigonometry #convergence-divergence
731
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Generating function of the sequence $\binom{2n}{n}^3H_n$

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#sequences-and-series #special-functions #generating-functions #hypergeometric-function
111
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Summing a simple series

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#sequences-and-series
65
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Convergence of unknown series

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#sequences-and-series #convergence-divergence
79
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Counter example for incorrectly formulated series convergence test statements

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#sequences-and-series #convergence-divergence
105
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Geometric represntation of terms for reccurence sequence with $f(x)=\frac{-1}{2} x+3$?

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#sequences-and-series #geometry #recurrence-relations
51
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Sequence of Riccati's roots

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#sequences-and-series #polynomials
108
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Limit of AM/GM ratio for large collections of numbers

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#sequences-and-series #limits #exponential-function #law-of-large-numbers
76
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The limit of $2\frac{\sin\left(\frac{M\theta_{k}}{2}\right)\cos\left(\frac{1}{2}(1+M)\theta_{k}\right)}{\sin\left(\frac{\theta_{k}}{2}\right)} $

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#probability #sequences-and-series #limits #trigonometry #fourier-transform

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