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Posted: September 5, 2010 03:24 am  | |||
      IRC Nickname: Gibble00 Group: Emeritus Posts: 775 Member No.: 100 Joined: January 3, 2008 Total Events Attended: 9    | Prove the following statement for all n >= 1. 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2 I can't do it. --------------------  | ||
Posted: September 5, 2010 08:41 am | |||
 IRC Nickname: DG_Keanu Group: Council Posts: 4782 Member No.: 2033 Joined: August 25, 2009 Total Events Attended: 173 | 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2 (1+2+...+n)^3 = (1+2+...+n)^2 X^3 = X^2 3 = 2 *head explodes* Sorry, haven't done maths in 2 years  --------------------  [05:42] <+WG_Keanu> I think I got a semi just looking at the pic [05:42] <%kat> same | ||
Posted: September 5, 2010 10:23 am | |||
| IRC Nickname: Rodney75 Group: Council Posts: 1683 Member No.: 2109 Joined: October 29, 2009 Total Events Attended: 154 | Tried proof by induction? --------------------  | ||
Posted: September 5, 2010 01:03 pm | |||
 IRC Nickname: megajayson Group: Elite Guardian Posts: 9246 Member No.: 423 Joined: April 4, 2008 Total Events Attended: 216 | Sounds like question is broke son --------------------  This is ten percent luck, twenty percent skill Fifteen percent concentrated power of will Five percent pleasure, fifty percent pain And a hundred percent reason to remember the name! 7th Highest Overall for Wars Attended. | ||
Posted: September 5, 2010 09:42 pm | |||
 IRC Nickname: chip54321 Group: Emeritus Posts: 532 Member No.: 119 Joined: January 11, 2008 Total Events Attended: 197 | Hey, this is just a problem with differences of cubes, its far simpler than it looks. note: difference of cubes states that x^3+y^3 = (x+y)(x^2-xy+y^2). So, lets only look at the last two terms on the Left Side, n and n - 1. So, we have n^3+(n-1)^3, which is equal to (by difference of cubes) = (n+n-1)(n^2-n^2-n+(n-1)^2) This simplifies to (2n-1)((2n-1), if you want, you can rearrange this to get (n+n-1)^2, which is basically the proof. If you want I can go further into it, or try to use a different trick to prove it, just post if you want any further info. --------------------      | ||
Posted: September 6, 2010 02:00 am | |||
 IRC Nickname: Maths Group: Ex-Member Posts: 1855 Member No.: 54 Joined: December 31, 2007 Total Events Attended: 286 | Seems like a rly gay proof by induction. --------------------  "Journeys are what brings us happiness, Not the destination." ~ Two time ex-raid leader of wg ~  | ||
Posted: September 6, 2010 02:59 am | |||
 IRC Nickname: [JC] Group: Emeritus Posts: 3320 Member No.: 23 Joined: December 30, 2007 Total Events Attended: 147 |
Wrong in the second line  Should be (the ... is not cubed): (1+2+n)^3+... = (1+2+....+n)^2 And thinking about it properly, you can't even put them in brackets as 1^2+2^2 will not give the same result as (1+2)^2 (5 vs. 9) --------------------  Old awards wat Most Mature & Most Honourable Most Dedicated|IRC Freak|Best Emeritus Placeholder lolz | ||
Posted: September 6, 2010 04:57 am | |||
| IRC Nickname: Gibble00 Group: Emeritus Posts: 775 Member No.: 100 Joined: January 3, 2008 Total Events Attended: 9 |
Awesome, this helped a lot. Thanks all. Best subforum ever. -------------------- | ||
Posted: September 14, 2010 01:11 am | |||
 IRC Nickname: Indivi2you Group: Elite Guardian Posts: 5361 Member No.: 43 Joined: December 30, 2007 Total Events Attended: 623 | L2precalc -------------------- The First, The Last, and the Only ~FLO Never say never, because limits, like fears, are often just an illusion. ~Michael Jordan      | ||
Math Proof