
#1
Feb208, 12:00 PM

P: 10

1. The problem statement, all variables and given/known data
Give an example of two monotonic sequences whose sum is not monotonic 2. Relevant equations nonoe 3. The attempt at a solution Well, I'm thinking is you just used n and n, would that be a valid attempt at the question, or is that just the lazy way out...... 



#2
Feb208, 12:17 PM

Sci Advisor
HW Helper
PF Gold
P: 4,768

It's no way out. A constant sequence is monotonic (just not "strictly monotonic")




#3
Feb208, 12:21 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882

So try n and a_{n} so that n+ a_{n} = n. What must a_{n} be?




#4
Feb208, 12:26 PM

P: 10

monotonic sequences
2n?




#5
Feb208, 01:43 PM

Sci Advisor
HW Helper
Thanks
P: 25,170

Just take a nonmonotonic sequence like, say (n10)^2=n^220*n+100 and try to split it into two monotonic parts that sum to the whole.




#6
Feb208, 01:59 PM

P: 10

ok, thanks man.




#7
Feb208, 03:11 PM

P: 31

a monotonic sequence is just a sequence of numbers that are either increasing or decreasing
so {1/x} is decreasing for x= 1 to infinity {1/x} is obviously increasing (becoming less negative for each term in the sequence) add them together= 0 whihc is just a constant...neither increasing or decreasing but steady. correect me if i'm wrong. 



#8
Feb208, 03:15 PM

Sci Advisor
HW Helper
PF Gold
P: 4,768

See post #2 nuclearrape. A constant sequence is monotonic by definition.




#9
Feb208, 03:16 PM

P: 31

post 2 is wrong...a constant function is not monotonic....READ the definition.




#10
Feb208, 03:24 PM

P: 420

A monotonic sequence is [tex]a_{n+1}\geq a_{n}[/tex] for all n. Notice the great than or equal to.




#11
Feb208, 03:30 PM

P: 31

increasing if an< an+1 for all n>1
decreasing if an+1< an for all n>1 monotonic if its either increasing or decreasing 



#12
Feb208, 03:31 PM

P: 420




#13
Feb208, 03:33 PM

P: 31

that website needs revision.




#14
Feb208, 04:25 PM

P: 420

So you're saying that mathworld is wrong, wikipedia is wrong, Rudin is wrong, the book I'm using for my adv calc class this semester is wrong, Apostle is wrong, and Shaum's Outline is wrong?
GG 



#15
Feb208, 04:35 PM

P: 31

no...wikipedia says this..."Functions that are strictly increasing or decreasing are onetoone (because for x not equal to y, either x < y or x > y and so, by monotonicity, either f(x) < f(y) or f(x) > f(y), thus f(x) is not equal to f(y))."




#16
Feb208, 04:36 PM

P: 31

when we talk about monotonic we are talking about strictly increasing or decreasing function...stop accusing me of saying that everyone is wrong...and just read a little bit.




#17
Feb208, 04:42 PM

P: 420

Scan of part of page 55 of Rudin's Principals of Mathematical Analysis 3rd edition: http://img228.imageshack.us/img228/7092/rudinud5.jpg 



#18
Feb208, 04:49 PM

P: 206

I've always understood that the definition of a monotonic sequence depended heavily on whose book/notes you happened to be reading at the time. Either way, both potential forms of the question have been answered, I believe, so why argue?



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