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Loser66
 one year ago
Explain me, please.
Loser66
 one year ago
Explain me, please.

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dan815
 one year ago
Best ResponseYou've already chosen the best response.2for a decreasing sequence bn that summation converges

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Those are what my prof did in class.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0The red parts are my explanation on the lecture so that I remember what is going on when reviewing for test. :)

dan815
 one year ago
Best ResponseYou've already chosen the best response.2it is still downloading, its going very slow

dan815
 one year ago
Best ResponseYou've already chosen the best response.2lets take cos(ntheta)= Real part of {e^(itheta)}

dan815
 one year ago
Best ResponseYou've already chosen the best response.2what they are using as their argument is that hey look just like how an alternating sequence of (1)^n multiplied by a decreasing series goes to 0, this also does the same thing

dan815
 one year ago
Best ResponseYou've already chosen the best response.2because for any thetea u pick, for varying n, you keep getting some number of positive and some number of negatives , both equal to each other, tho the addition of this decreasing bn sequences works slightly differently

dan815
 one year ago
Best ResponseYou've already chosen the best response.2but you can still definately show that you will be subtracting greater part than what u are adding in the next set

dan815
 one year ago
Best ResponseYou've already chosen the best response.2here is a picture to help you see

dan815
 one year ago
Best ResponseYou've already chosen the best response.2varying theta is just like varying the period you sample your dots

dan815
 one year ago
Best ResponseYou've already chosen the best response.2so in fact this is not much different from alternating series at all, its just put in a different way

dan815
 one year ago
Best ResponseYou've already chosen the best response.2let f(n) be some decreasing function for the first 3 values of n let cosntheta be positive for the next 3 values of n let cos n*theta be negative can you see why now, this has to be convergin

dan815
 one year ago
Best ResponseYou've already chosen the best response.2liket lets take a random decreasing function

dan815
 one year ago
Best ResponseYou've already chosen the best response.2thats wht u are doing with chos (ntheta) you are taking samples in each part of that curve adding and subtracting

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0dan, slow down on let f(n) be some decreasing function for the first 3 values of n let cosntheta be positive for the next 3 values of n let cos n*theta be negative can you see why now, this has to be convergin

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0f(n) = cos (ntheta) 3 values of n let cos n theta > 0

dan815
 one year ago
Best ResponseYou've already chosen the best response.2these could be your sambled points when you multiply by cos n theta

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0They are the value of cos (n theta) when n = 1, 2, 3... right?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2now you say the sum of all these samples values in between is bounded by that formula they gave u up at the top

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0suppose 0<theta < pi, then it limits on dw:1441646174573:dw

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0sum cos (n theta) = cos (0theta) + cos (1 theta) + cos (2 theta) + ..... cos (ntheta) , right? then?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0is it not that it is =0?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2now u can use that bound

dan815
 one year ago
Best ResponseYou've already chosen the best response.2notice how if theta >0 its going to finity as u will be sampling an infinite points in each of the interval

dan815
 one year ago
Best ResponseYou've already chosen the best response.2@empty how do u show this series converges

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Is it not that if it is bounded and continuous, it converges?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2its kind of weird to think about actually

dan815
 one year ago
Best ResponseYou've already chosen the best response.2like say you take an finite number of points on the highest parto of your decreasing function

dan815
 one year ago
Best ResponseYou've already chosen the best response.2now lets say u subtract an infinite set of points but lesser value.. the difference between these 2 is still infinity is it notq

dan815
 one year ago
Best ResponseYou've already chosen the best response.2but then u subtraced with some other difference an infinite set of points when compared to the next block of addition

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0I gotta go. You guys PPPPPPLLLLLEASE, freely discuss. I' ll take it later. Thanks in advance.
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