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What does $x-a$ do in Taylor series?

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#calculus #sequences-and-series #polynomials #taylor-expansion
100
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Is the sequence $a_{n}= {{n}\choose{[n/2]}}^{1/n}$ increasing?

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#calculus #sequences-and-series #binomial-coefficients #monotone-functions
1.6k
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Uniform convergence of $\sum e^{-xn^2}$

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#real-analysis #sequences-and-series #convergence-divergence #summation #uniform-convergence
76
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Limiting a positive sequence that goes to zero.

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#real-analysis #sequences-and-series
53
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Inductive relation for the Harmonic series

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#sequences-and-series #elementary-number-theory
1k
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Formula to get a unique combination for N values from 0 to (N-1)?

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#sequences-and-series #combinations
87
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In a G.P. the sum of the first five terms is $80$, if the difference between the sixth and first term is $5$, find the first term and common ratio.

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#sequences-and-series
62
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Is there anything in the proof for $\frac{a}{1-r}$ to show that it won't work for $|r|\gt1$ when summing an infinite geometric series?

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#sequences-and-series #convergence-divergence #geometric-series
98
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Is my proof that $\sum_{n=3}^\infty \log(\frac{n^2+n+1}{n^2})$ diverges correct?

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#real-analysis #sequences-and-series #convergence-divergence #solution-verification
41
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find a sequence with the following properties

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#calculus #sequences-and-series
622
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Calculating the summation $\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}$

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#sequences-and-series #harmonic-numbers
417
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How was the integral formula for the binomial coefficient discovered?

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#sequences-and-series #combinatorics #binomial-coefficients #math-history
514
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Does $a_n = n\sin n$ have a convergent subsequence?

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#real-analysis #sequences-and-series #convergence-divergence
195
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Computing the sum $\frac{1}{(\frac{1}{n}-p)^{2}}+\frac{1}{(\frac{2}{n}-p)^{2}}+\ldots+\frac{1}{(1-p)^{2}}$

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#probability #sequences-and-series #algebra-precalculus #summation #expectation
1.3k
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How to investigate the uniform convergence of the series

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#sequences-and-series #uniform-convergence

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