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The convergence of power series of $\log(1+x)$ with or without Taylor expansion

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#real-analysis #logarithms #power-series #taylor-expansion
112
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Power series formed by terms of a null sequence

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#real-analysis #sequences-and-series #convergence-divergence #power-series
389
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find ln 0.97 with 7 decimal place accuracy

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#calculus #power-series #approximation
76
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Differentiating infinite series

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#real-analysis #sequences-and-series #derivatives #power-series
75
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Question on Uniform Convergence of a Sum

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#real-analysis #power-series #uniform-convergence
75
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Evaluate $\sum_{n=1}^\infty(-1)^{n-1}\frac{9}{4^n}.$

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#calculus #summation #power-series
64
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$\sum_{n=1}^\infty (n^2+n)(x-1)^n$ closed form

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#real-analysis #power-series #taylor-expansion
43
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Finding a function f with information of its power series

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#real-analysis #convergence-divergence #power-series
30
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find the Maclaurin expression

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#calculus #power-series
28
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Evaluate the maclaurin series from $0$ to $1.5$ with an error less than 0.0001

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#calculus #power-series
80
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Solving a 2nd order DE (non-constant coefficients)

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#ordinary-differential-equations #power-series
47
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Radius of convergence: $\sum\limits_{n=0}^{\infty} \frac{n!x^n}{100^n}$

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#power-series
285
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interval and radius of convergence of Maclaurin series: $(-1)^{n+1} (|(1-x)/(1+x)|-1)^n)/n$

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#calculus #power-series #taylor-expansion
320
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Inner product spaces, orthogonality, complex integration and non-uniform convergence

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#functional-analysis #power-series #inner-products #uniform-convergence #complex-integration
1.3k
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Power series expansion of $\text{arsinh}(x)$ at $0$

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#analysis #functions #power-series #taylor-expansion #hyperbolic-functions

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