Name the test used to show convergence/divergence
Sums
Justification
What is the limit?
Converge or diverge and why?
100
sum1/n^2
What is the p-series test?
100
Find the sum of the series:
10 - 20/3 + 40/9 - 80/27 + ...
What is 6?
100
What words need to be written any time you apply the integral test?
What are "the series is positive, continuous and decreasing" ?
100
lim_(n->oo)(-2/5)^n
What is 0?
100
sum_(n=0)^oo(2/3)^n
What is the series converges by geometric series test ? (|r| = 2/3 < 1)
200
sum (5^n)/(n!)
What is the ratio test?
200
Find the sum
What is 14/3 ?
200
What words need to be written any time you apply the alternating series test or the alternating series remainder theorem?
What is "The terms of the series alternate in sign and decrease in absolute value to 0" ?
200
lim_(n->oo)(3n)/(n+1
What is 3?
200
sum_(n=0)^oo(-1)^n2^n/(n!)
What is the series converges by alternating series test ?
(must show the limit and have the statement, "the terms of the series alternate in sign and decrease in absolute value")
300
sum (2/3)^n
What is the geometric series test?
300
Write 0.9273273273273273... as a geometric series in sigma notation
What is
300
There are three tests that prove convergence when the limit value is less than 1 and divergence when the limit value is greater than 1. Name these three tests.
What are the geometric, ratio and root tests?
300
lim_(n->oo)(2^n)/(n!)
What is 0?
300
sum_(n=0)^oo(-1)^n(n!)/2^n
What is the series diverges by nth term test ?
(Must show the limit is DNE)
400
sum (lnn)/n
What is the integral test?
400
Find the sum (no calculators)
What is 81/140 ?
400
The terms of a series are:
4 - 8/3 + 4/3 - 8/15 + 8/45 - ...
If the first 3 terms are used to approximate the sum of the series, explain why the error in the approximation must be less than 2/3.
What is:
The terms of the series alternate in sign and decrease in absolute value to 0.
Error ≤ |-8/15| < 2/3 :)
400
lim_(n->oo)sin((npi)/2)
What is DNE?
400
sum_(n=0)^oo(n^2-2)/(n^5)
What is the series converges either by direct or limit comparison?
(must either show the inequality or the limit)
500
sum n/(n^3+5)
What is the direct or limit comparison test?
500
Write 1.2494949494949494949... as a fully simplified quotient of two integers (no calculators)
What is 1237/990?
500
If the
lim_(n->∞)|a_n|=0
then the series converges: a) absolutely, b) conditionally or c) cannot be determined with the information given
What is c) cannot be determined with the information given
500
lim_(n->oo)(1-2/n)^n
What is e-2?
500
sum_(n=3)^oo(lnn/n)
What is the series diverges by integral test ?
(Must include the statement "the function f(x) = lnx/x is positive, continuous and decreasing" and show the improper integral using correct limit notation)