What is an infinite sequence in mathematics?
An infinite sequence is an ordered list of numbers indexed by integers.
Sequence limit
Sequence terms approach L as n→∞.
When does a sequence a_n converge to a limit L?
When its terms become arbitrarily close to L as n becomes large.
Monotone + bounded
Always convergent sequences.
What defines a monotonic sequence?
It is either increasing with a_n < a_(n+1) or decreasing with a_n > a_(n+1).
Geometric sum convergence
Converges if |r|<1; sum = a/(1-r).
What does every bounded monotonic sequence do?
It converges.
Series divergence test
Diverges if terms don't tend to zero.
Partial sum
Sum of first n terms of series.
Power series
Infinite sums with variable x.
Taylor series
Series expansion of functions about a point.
Pon a prueba tus conocimientos con 10 preguntas sobre Infinite Series and Taylor Methods.
1. What mathematical object is an infinite sequence?
2. What is a sequence in mathematical terms?
Revisa el curso completo en la hoja de repaso para Infinite Series and Taylor Methods.
Ver hoja de repaso →Importa tu curso y la IA genera tarjetas de memoria en 30 segundos.
Generador de tarjetas de memoria