Series and Convergence flashcards
22 practice cards drawn from the Series and Convergence lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the Series and Convergence lessons in full →
splits into
from “Sums of Squares and Cubes”
equals
36
from “Sums of Squares and Cubes”
As n grows without bound, tends to
1
from “The Method of Differences”
equals
from “The Method of Differences”
Terms shrinking to zero proves
nothing on its own
from “The nth Term Test for Divergence”
What does the nth term test say about ?
it diverges
from “The nth Term Test for Divergence”
converges exactly when
p > 1
from “The p-Series”
Does converge or diverge?
diverges
from “The p-Series”
is best compared with
from “Comparison Tests for Series”
and diverges, so
diverges
from “Comparison Tests for Series”
The alternating series test needs the sizes to
fall to zero
from “The Alternating Series Test”
The series is
conditionally convergent
from “The Alternating Series Test”
By the ratio test,
converges
from “The Ratio Test”
When L = 1, the ratio test
decides nothing
from “The Ratio Test”
The radius of convergence of is
1
from “Radius and Interval of Convergence”
The radius of convergence of is
from “Radius and Interval of Convergence”
The Maclaurin series of ln(1 + x) begins
from “The Standard Maclaurin Series”
expands as
from “The Standard Maclaurin Series”
The Taylor series of ln x about a = 1 begins
(x − 1)
from “Taylor Series About a Point”
Term n of a Taylor series about a is
from “Taylor Series About a Point”
Approximating sin x by its degree-3 polynomial on , the error is at most
from “The Lagrange Error Bound”
In the Lagrange bound, M stands for
an upper bound for the next derivative
from “The Lagrange Error Bound”