Computer Forums I solved it!

 07-06-2005, 12:57 PM #1 Golden Master     Join Date: Oct 2004 Posts: 5,810 I solved it! well, she is gone, (chick) but she did challenge me. She asked me this question: Let xn and yn be two sequences with the following properties: >x_(n+1)=xn2+yn2 and y_(n+1)=2*xn*yn for any n>=1 and x1 and y1>0. >Prove that the series zn=xn/yn converges. and.... I found that every term zn is greater than 1 so the sum of the series must diverge. x(n+1) z(n+1) = ------- > 1 (aassume this to be true) y(n+1) xn2 + yn2 ----------- > 1 2.xn.yn xn2 + yn2 > 2.xn.yn xn2 - 2.xn.yn + yn2 > 0 (xn - yn)2 > 0 This is always true since a perfect square must be positive. It follows that z(n+1) > 1. If the zn terms are all greater than 1 the series must diverge. Yes!!! __________________ __________________ Macbook Pro and Logitech z5500s. All you really need.
 07-06-2005, 01:10 PM #2 In Runtime     Join Date: Jun 2005 Posts: 114 Re: I solved it! yea, thats what i figured.....i didnt even think that was a real question, how much math did you take in school? __________________ __________________ This space for rent.
 07-06-2005, 01:15 PM #3 Golden Master     Join Date: Oct 2004 Posts: 5,810 Re: I solved it! Well, I'm trying not to be racist... but I am asain. I'm only in the 10th grade, but I have already studied calculus and the like. So yeah. It took me a while... but there you go. Of course, I'm not a math genius or anything. No where near Einstein or Gauss or people like them. I just work hard, I guess. __________________ Macbook Pro and Logitech z5500s. All you really need.
 07-06-2005, 01:18 PM #4 Site Team     Join Date: Mar 2004 Posts: 8,098 Re: I solved it! maths good... spelling bad... Asian, Race has nothing to do with intelligence. __________________
 07-06-2005, 01:22 PM #5 Golden Master     Join Date: Oct 2004 Posts: 5,810 Re: I solved it! I know... but you have to admit... Korea is ranked no.2 in the world as being the best at math. I think New Zealand is no.1 so yeah. Japon and China are just behind Korea, like no.3 and 4 I think. As I said, I wasn't being racist, just going off the statistics... __________________ Macbook Pro and Logitech z5500s. All you really need.
 07-06-2005, 02:08 PM #6 Fully Optimized   Join Date: May 2005 Posts: 1,690 Re: I solved it! Let xn and yn be two sequences with the following properties: x_(n+1)=xn^2+yn^2 and y_(n+1)=2*xn*yn for any n>=1 and x1 and y1>0. Prove that the series zn=xn/yn converges. Let a_n be x_n/y_n. Then a_(n+1)=x_n/2y_n+y_n/2x_n=(a_n+1/a_n)/2. But a_n>=1 for any n>=2, so 1/a_n <= a_n, so a_(n+1) <= a_n. From the fact that a_n >0 for any n we get that (a_n) is a decreasing sequence which also has a lower bound, so it's convergent. __________________
 07-06-2005, 02:11 PM #7 Fully Optimized   Join Date: May 2005 Posts: 1,690 Re: I solved it! Lets put a check on the racism stuff...before it gets out of hand. __________________
 07-06-2005, 02:12 PM #8 Golden Master     Join Date: Oct 2004 Posts: 5,810 Re: I solved it! Yeah yeah, I know. I'm done. __________________ Macbook Pro and Logitech z5500s. All you really need.
 07-06-2005, 02:19 PM #9 BSOD     Join Date: Jan 2005 Posts: 1,386 Re: I solved it! O_O that hurts my head. is that algebra or physics or calulus or what? __________________
 07-06-2005, 02:30 PM #10 BSOD   Join Date: Jul 2005 Posts: 2 Re: I solved it! . __________________ __________________