CONDITIONS + EVALUATION
What does the geometric series test say about the common ratio in order for the series to converge/diverge?
The series converges if the absolute value of the common ratio is less than 1 and the series diverges if the absolute value of the common ratio is greater than or equal to 1.
∑(4n^2−n)/(n^3+9)
1/n
∑(1/n^2)
P series test
What test do you use to find the radius of convergence?
Ratio test
For the p series test, what does p have to be in order for the series to diverge?
If p is less than or equal to 1, the series diverges
∑(√2n^2+4n+1)/(n^3+9)
1/n^2
∑(e/pi)^n
Geometric series test
FIND THE GENERAL TERM OF THIS POWER SERIES CENTERED AT X=2 1/1-X FORMAT!!!
What makes a series absolutely converge and what makes it conditionally converge?
If the absolute value of the series converges, then the series converges absolutely.
What must the answer of the limit be in order for the series to converge for the limit comparison test?
The answer must be finite and positive.
∑(3e^−n)/(n^2+2n)
1/n^2
∑(n^2/(n^3+1))
Integral test, limit, or direct comparison
FIND THE GENERAL TERM
What is the formula to find the sum of the geometric series?
a/(1-r)
What are the conditions that must be stated to use the AST and what makes the series converge?
Terms alternate in sign and decrease in magnitude to zero AND the limit equals zero.
∑1/(nlnn)
Integral test
INTEGRAL OF GENERAL
What is the alternating series error?
The error/remainder is less than the absolute value of the first neglected term
What do you have to state to do the Integral Test and what makes it converge or diverge?
f(x) is positive, continuous, and decreasing. If the integral is a number then the series converges. If the integral is infinity then the series diverges.
∑((3n+1)/(4−2n))^2n
Root test
DERIVATIVE OF GENERAL TERM
How do you determine if a sequence converges or diverges?
If the limit of the sequence exists, then the sequence converges. If the limit of the sequence does not exist, then the sequence diverges.