Direct & Limit Comparison
We are using limit comparison test. If we know that the limit of a_n/b_n equals a finite c-value and b_n converges, what can we say about a_n?
a_n converges
To use the alternating series test, what two things must be true in order to use it?
The terms must decrease; the limit equals zero
We are using ratio test. If we find that the limit is equal to 1, what is the result of our test?
inconclusive
Use the ratio or the root test to determine the radius of convergence. Determine the interval of convergence.
sum _{n=0}^infty x^n
R = 1; I = (-1, 1)
Name one instrument that Tim plays.
drums, piano, guitar, bass
Use the limit comparison test to determine if the follwing series converges or diverges.
sum _{n=1}^infty \frac{n^2-2n+1}{n^4+27n^3+1}
converges
Determine if the following series converges or diverges
sum _{n=0}^infty \frac{(-1)^n}{n!}
converges by alternating series test
Determine if the series converges absolutely, converges conditionally, or diverges.
sum _{n=1}^infty (\frac{x}{e^n})^n
By the root test, the series converges absolutely.
Use the ratio or the root test to determine the radius of convergence. Determine the interval of convergence.
sum _{n=1}^infty \frac{x^n}{e^{n^2}}
R = infty
I = (-infty, infty)
What are the names of Snow White's seven dwarves?
Doc, Happy, Grumpy, Sleepy, Sneezy, Bashful, and Dopey
Use the direct comparison test to determine if the follwing series converges or diverges.
sum _{n=1}^infty \frac{4^n+3}{5^n+n}
converges
Determine if the following series converges absolutely, converges conditionally, or diverges.
sum _{n=1}^infty \frac{(-1)^{n+1}ln(n)}{sqrt(n)}
converges conditionally
Determine if the series converges absolutely, converges conditionally, or diverges.
sum _{n=1}^infty \frac{(-3)^{3n}}{n^n}
By the root test, the series converges absolutely.
Use the ratio or the root test to determine the radius of convergence. Determine the interval of convergence.
sum _{n=0}^infty n!(3x-2)^n
R = 0
I = {\frac{2}{3}}
In which Italian city did pizza originate?
Naples
Determine if the follwing series converges or diverges.
sum _{n=3}^infty \frac{(n+1)^\frac{3}{2}}{3n+4}
diverges by LCT
Determine if the following series converges absolutely, converges conditionally, or diverges.
sum _{n=1}^infty (\frac{ln(n)}{sqrt(n)})^2
converges conditionally
Determine if the series converges absolutely, converges conditionally, or diverges.
sum _{n=1}^infty \frac{n!}{e^{n^2}}
By the ratio test, the series converges absolutely
Use the ratio or the root test to determine the radius of convergence. Determine the interval of convergence.
sum _{n=0}^infty (-1)^n \frac{(x-3)^{2n}}{n*5^n}
R = 5
I = (-2, 8]
What does NASA stand for?
National Aeronautics and Space Administration
Determine if the follwing series converges or diverges.
sum _{n=3}^infty \frac{ln(n)+cos(n)}{n^2}
converges by direct comparison test
Determine if the series converges absolutely, converges conditionally, or diverges.
sum _{n=1}^infty \frac{(-4)^n*n^2}{n!}
By the ratio test, the series converges absolutely
Use the ratio or the root test to determine the radius of convergence. Determine the interval of convergence.
sum _{n=0}^infty \frac{(-1)^n*x^{2n}}{2^{2n}(n!)^2}
R = infty
I = (-infty, infty)
What are people with Alektorophobia afraid of?
Chickens