New posts in taylor-expansion

Taylor formula uniqueness for multivariate maps

real-analysis taylor-expansion

How do you create an alternating series with the sign being the same twice in a row?

calculus sequences-and-series power-series taylor-expansion

computing the series $\sum_{n=1}^\infty \frac{1}{n^2 2^n}$

sequences-and-series taylor-expansion

Taylor expansion of $(1+x)^α$ to binomial series – why does the remainder term converge?

calculus real-analysis power-series taylor-expansion

How to calculate the series $-\frac12-\frac14+\frac13-\frac16-\frac18+\frac15-\frac{1}{10}...$?

calculus limits summation taylor-expansion

What is the remainder for a taylor series of two variables.

multivariable-calculus taylor-expansion

Why do the endpoints of the Maclaurin series for arcsin converge?

calculus taylor-expansion

Where do the factorials come from in the Taylor series?

calculus taylor-expansion

Series expansion of infinite series raised to the $n$th power

sequences-and-series taylor-expansion multinomial-coefficients

Why does this infinite series equal one? $\sum_{k=1}^\infty \binom{2k}{k} \frac{1}{4^k(k+1)}=1$

calculus sequences-and-series limits binomial-coefficients taylor-expansion

Infinitely differentiable function with divergent Taylor series?

real-analysis convergence-divergence taylor-expansion

Laurent series for $\cot (z)$

complex-analysis taylor-expansion residue-calculus laurent-series

Maclaurin series for $\frac{x}{e^x-1}$

sequences-and-series taylor-expansion

Relationship Between Sine as a Series and Sine in Triangles

calculus trigonometry taylor-expansion trigonometric-series

How do Taylor polynomials work to approximate functions?

calculus sequences-and-series taylor-expansion

How to proof that smooth function vanishing on xy-coordinates cross must be of form $xyg$?

real-analysis multivariable-calculus taylor-expansion smooth-functions

Dividing an infinite power series by another infinite power series

taylor-expansion rational-functions

$x^3-3x-3=0$, prove that $10^x<127$

inequality logarithms taylor-expansion

Taylor Series of $\tan x$

taylor-expansion trigonometric-series

Under what conditions is integrating over a series expansion valid for an improper integral?

sequences-and-series taylor-expansion improper-integrals