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

You are not logged in. #26 20121005 04:30:17
Re: Prove this
That would be just incarefullness. The steps are not equivalent. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #27 20121005 04:31:19
Re: Prove thisHi Agnishom The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #28 20121005 12:59:49
Re: Prove thisHi All! Last edited by noelevans (20121007 13:33:47) Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #29 20121005 22:23:12
Re: Prove thisI know what AMGM inequality is but have not made a lot of its use. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #30 20121006 03:50:01
Re: Prove this
Then you should know that for two real numbers it states that . Now set x=n and y=1/n. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #31 20121006 14:51:52
Re: Prove thisOh! Great! 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #32 20121202 12:05:21
Re: Prove thisOne more question: Last edited by Agnishom (20121202 12:14:02) 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #33 20121202 13:25:24
Re: Prove thisI think you require to be positive as well. Let and . Then is convex for . Applying Jensen's inequality gives which is what's required. Last edited by scientia (20121202 14:47:21) #34 20121202 13:41:50
Re: Prove thisIs there any other way than using derivatives? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #35 20121202 14:47:46
Re: Prove thisWhat derivatives? 