Fundamental Power Series of Mathematical Functions Flashcards (12 cards)

Series for e^x converging for all real x.

Sum of $x^{2n+1}/(2n+1)$! for all real x.

Sum of $x^{2n}/(2n)$! for all real x.

Sum of $(-1)^n x^{2n+1}/(2n+1)$! for all real x.

Sum of $(-1)^n x^{2n}/(2n)$! for all real x.

Convergence depends on radius and boundary points.

$-∑_{n=1}^∞ x^n/n$, for x in ]-1, 1[.

$∑_{n=0}^∞ (-1)^n x^{n+1}/(n+1)$, for x in ]-1, 1[.

$1/(1-x) = ∑_{n=0}^∞ x^n$, for |x|<1.

$1/(1+x) = ∑_{n=0}^∞ (-1)^n x^n$, for |x|<1.

Distance from center where series converges.

Must check separately; may diverge or converge.