How do we guess some equations like
1^2 + 2^2 + 3^2 + ... + n^2 is equal to [n(n + 1)(2n + 1)]/6
and
1 x 3 + 3 x 5 + 5 x 7 + ... + (2n - 1)(2n + 1) is equal to [(2n - 1)(2n + 1)(2n + 3) + 3]/6
before we prove it? Is it by trial and error?
How do we guess some equations like 1^2 + 2^2 + 3^2 + ... + n^2 = [n(n + 1)(2n + 1)]/6 before we prove it?
2010-10-06 2:57 pm
回答 (2)
2010-10-06 3:02 pm
✔ 最佳答案
I got into a big argument with someone on this and he proved me wrong he was able to derive formulaI will check my e-mails
tada I Sponcered and I both derived it here....
http://answers.yahoo.com/question/index?qid=20100408132419AAJ3fyS
參考: R
2010-10-06 10:02 pm
These formulas were derived years ago, by tedious computations and by using the guess-and-check method or something like that.
Proving them involves mathematical induction.
Proving them involves mathematical induction.
收錄日期: 2021-05-01 13:03:17
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101006065734AARUmTi