Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

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Re: Jane’s exercisesTo 10 : Last edited by Stanley_Marsh (20070412 17:22:40) Numbers are the essence of the Universe #27 20070412 18:40:20
Re: Jane’s exercisesThe a_{n} have to be rational numbers. Are they? #28 20070413 00:44:16
Re: Jane’s exercisesAwwwww , Let me come up with another one. Numbers are the essence of the Universe #29 20070413 02:07:16
Re: Jane’s exercisesYou’d be surprised – it’s actually much simpler than you think. #30 20070413 07:16:53
Re: Jane’s exercisesWhat about Riemann zetafunction I happened to see the Riemann zetafunction today~lol Last edited by Stanley_Marsh (20070413 07:17:10) Numbers are the essence of the Universe #31 20070413 07:18:57
Re: Jane’s exercises9 ,11 are hard for me , I haven't that much knowledge of math , I just learn math randomly by myself .haha Numbers are the essence of the Universe #32 20070413 07:51:34
Re: Jane’s exercises
... like a ti92+ or voyage 200 ; ) #33 20070413 08:27:24
Re: Jane’s exercises
Yes, that’s fine. In fact, you’ve found a required example. The sequence is bounded above (e.g. 2 is an upper bound), it is increasing, and the a_{n} are rational – but is not rational. Last edited by JaneFairfax (20070413 14:12:50) #34 20070413 08:42:54
Re: Jane’s exercisesMy TI89 does it... I know a guy with a 92, the thing is huge. #35 20070413 13:58:27
Re: Jane’s exercisesBrilliant! I’m glad you spotted the trick. Last edited by JaneFairfax (20070413 14:05:41) #36 20070416 05:58:16#37 20070416 06:18:24
Re: Jane’s exercisesLast edited by Stanley_Marsh (20070416 06:26:09) Numbers are the essence of the Universe #38 20070416 06:25:44
Re: Jane’s exercisesOh , forget it , Numbers are the essence of the Universe #39 20070416 06:39:54#40 20070416 06:50:26
Re: Jane’s exercisesWhat’s more, is false. Try a = b = 0, k = 1⁄2. And You mean the Cauchy–Schwarz inequality? Last edited by JaneFairfax (20071219 13:51:06) #41 20070416 10:51:25
Re: Jane’s exercisesI think I got it Last edited by Stanley_Marsh (20070416 10:59:56) Numbers are the essence of the Universe #42 20070416 19:30:39
Re: Jane’s exercises
Sorry, I don’t get you here. Last edited by JaneFairfax (20070416 19:31:13) #43 20070417 07:54:01
Re: Jane’s exercisesactually , the first part ( They are all positive) The first part can be done by U can also think that a,b,c are distinct , Last edited by Stanley_Marsh (20070417 08:03:07) Numbers are the essence of the Universe #44 20070417 08:04:11
Re: Jane’s exercisesOkay for the first part, but I’m still not happy with the division bit in the second part. If you’re gonna divide, you should make sure you’re not dividing by zero. #45 20070417 08:10:58
Re: Jane’s exercisesWhat about Numbers are the essence of the Universe #46 20070417 08:19:34#47 20070426 07:00:24
Re: Jane’s exercises#13 Last edited by JaneFairfax (20070426 19:36:08) #48 20070426 10:15:42
Re: Jane’s exercisesDon't know it will work tho. Numbers are the essence of the Universe #49 20070426 20:07:06
Re: Jane’s exercisesI forgot to state that the three vectors a,b,c must be distinct (I’ve edited my post and added it now). #50 20070428 01:30:06
Re: Jane’s exercisesI have to dicuss those situation separately . Hmmm..... Numbers are the essence of the Universe 