04 Aug '08 12:26>
Prove that for any positive integer n
n cubed equals the sum of n sequential odd numbers
eg 4^3 = 64 = 13 + 15 + 17 + 19
n cubed equals the sum of n sequential odd numbers
eg 4^3 = 64 = 13 + 15 + 17 + 19
Originally posted by crazyblue1^3 = 1 = 1
isnt 3 a positive integer? 3^3 = 27 and i dont see how 4 odd numbers can add up to another odd number. am i missing something, or did you mean any _even_ positive integer?
Originally posted by geepamoogleproofing aside,....... because i can't do it๐........That is pretty cool๐ฒ
1^3 = 1 = 1
2^3 = 8 = 3 + 5
3^3 = 27 = 7 + 9 + 11
4^3 = 64 = 13 + 15 + 17 + 19
5^3 = 125 = 21 + 23 + 25 + 27 + 29
Pattern continues.
Prove that the sum of the first n cubes is the square of the sum of the first n numbers.
Originally posted by DejectionMy wife doesn't like latex. She's more into ... well, that's personal...
Ooo geep i love that relation. I especially like how it doesn't generalize to higher powers. Can be proven via induction(boring and ugly), telescoping(could be messy), a nice substitution (pretty cool), and geometrically (very awesome).
Sum(i^3, i, 1, n)=Sum(i, i, 1, n)^2 Would look better if we had LATEX.