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Conditions for the convergence of :$\cos\left( \sum_{n\geq0}{a_n}x^n\right)$

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#convergence-divergence #power-series
2.3k
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Power series solution of $y''+e^xy' - y=0$

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#ordinary-differential-equations #power-series
62
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Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$

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#real-analysis #sequences-and-series #analysis #convergence-divergence #power-series
82
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Pointwise and uniform convergence of function series $f_n = x^n$

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#real-analysis #convergence-divergence #power-series
108
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Divergence of power series at the edge

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#real-analysis #limits #power-series
527
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Maclaurin polynomial estimating $\sin 15°$

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#power-series #taylor-expansion
211
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Computing:$\sum_{n=0}^\infty\frac{3^n}{n!(n+3)}$

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#calculus #real-analysis #sequences-and-series #summation #power-series
84
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How to I find the Taylor series of $\ln {\frac{|1-x|}{1+x^2}}$?

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#calculus #real-analysis #algebra-precalculus #power-series #taylor-expansion
109
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Convergence radius of power series can be derived from root and ratio test.

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#real-analysis #analysis #convergence-divergence #power-series
162
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Recognizing recursion relation of series that is solutions of $y'' + y' + x^2 y = 0$ around $x_0 = 0$.

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#sequences-and-series #ordinary-differential-equations #power-series #recursion
127
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Radius of convergence about a different point

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#real-analysis #power-series
454
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Let $a_n$ be a decreasing sequence. Prove that the power series $\sum a_n x^n$ has no roots in $A=\{z\in C:|z|<1\}$

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#complex-analysis #power-series
76
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McLaurin expansion

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#sequences-and-series #ordinary-differential-equations #derivatives #power-series #taylor-expansion
117
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Find the sum of infinite series

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#real-analysis #sequences-and-series #definite-integrals #summation #power-series
96
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For what values of $z$ is $\sum_{n=0}^\infty\frac{z^n}{1+z^{2n}}$ convergent?

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#complex-analysis #convergence-divergence #power-series

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