Will I get Top 5 in Reaper Game 52?
by EpicSkills32, Jan 21, 2016, 5:04 AM
hm?
Probably not unless I get a few more +1hour reaps (which I have gotten more than one of) but some days I don't reap at all so idk.
I just found this out 2 days ago, but the music from One Punch Man was released Jan 13!
I clearly don't have enough motivation or willpower to post more frequently.
So much for posting all my notes from Math 1C. . .
I got a 47/50 on our first quiz, and the first (might be only) midterm is a week from today.
I'm gonna post all the tests we've learned so far:
is convergent, then 
Based on the above, we use the contrapositive:
If the
or DNE, then is divergent.
be a sequence of positive terms. Suppose that 
, where f is a continuous, positive, decreasing function of x for all 
(where N is a positive integer).
Then the series
and the integral 
either both converge or both diverge.
, 
, and 
be series of nonnegative terms.
Suppose that for some integer N:
for all 
.
(a) If
is convergent, then is also convergent.
(b) If
is divergent, then is also divergent.
and 
for all 
.
If
then 
and 
either both converge or both diverge. (Note: if c is infinity, the test doesn't work, but if the limit really is infinite, it should be clear from the beginning)
or 
The series
converges if all of the following conditions are satisfied:
(1) All the terms
are positive.
(2) The terms are eventually non increasing.
(3)
Define a series to converge absolutely if the corresponding series of absolute values 
is convergent.
be any series and suppose that 
, then:
(a) the series converges absolutely if
.
(b) the series diverges if
.
(c) the test is inconclusive if
.
be any series and suppose that ![$\lim_{n\to\infty} = \sqrt[n]{|a_n|} = \rho $](//latex.artofproblemsolving.com/6/d/8/6d8a5f2e091a786f1600c117ab7835f7fc07a91d.png)
(a) the series converges absolutely if.
(b) the series diverges if or is infinite.
(c) the test is inconclusive if
.
I'm too lazy to post examples right now. I really need to practice piano anyway.
Probably not unless I get a few more +1hour reaps (which I have gotten more than one of) but some days I don't reap at all so idk.
I just found this out 2 days ago, but the music from One Punch Man was released Jan 13!
I clearly don't have enough motivation or willpower to post more frequently.
So much for posting all my notes from Math 1C. . .
I got a 47/50 on our first quiz, and the first (might be only) midterm is a week from today.
I'm gonna post all the tests we've learned so far:
- Nth term Test
is convergent, then 
Based on the above, we use the contrapositive:
If the
or DNE, then is divergent.- Integral Test
be a sequence of positive terms. Suppose that 
, where f is a continuous, positive, decreasing function of x for all 
(where N is a positive integer).Then the series
and the integral 
either both converge or both diverge.- (Direct) Comparison Test
, 
, and 
be series of nonnegative terms.Suppose that for some integer N:
for all 
.(a) If
is convergent, then is also convergent.(b) If
is divergent, then is also divergent.- Limit Comparison Test
and 
for all 
.If
then 
and 
either both converge or both diverge. (Note: if c is infinity, the test doesn't work, but if the limit really is infinite, it should be clear from the beginning)- Alternating Series Test
or 
The series
converges if all of the following conditions are satisfied:(1) All the terms
are positive.(2) The terms are eventually non increasing.
(3)
Define a series
to converge absolutely if the corresponding series of absolute values 
is convergent.- Ratio Test
be any series and suppose that 
, then:(a) the series converges absolutely if
.(b) the series diverges if
.(c) the test is inconclusive if
.- Root Test
be any series and suppose that ![$\lim_{n\to\infty} = \sqrt[n]{|a_n|} = \rho $](http://latex.artofproblemsolving.com/6/d/8/6d8a5f2e091a786f1600c117ab7835f7fc07a91d.png)
(a) the series converges absolutely if
.(b) the series diverges if
or is infinite.(c) the test is inconclusive if
.I'm too lazy to post examples right now. I really need to practice piano anyway.
This post has been edited 2 times. Last edited by EpicSkills32, Jan 21, 2016, 5:07 AM
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