Mathematics Stack Exchange Q A for people studying math at any level and professionals in related fields
Prove that $1^3 + 2^3 + . . . + n^3 = (1+ 2 + . . . + n)^2$ Do you know a simpler expression for $1+2+\ldots+k$? (Once you get the computational details worked out, you can arrange them more neatly than this; I wrote this specifically to suggest a way to proceed from where you got stuck )
linear algebra - How to tell if a set of vectors spans a space . . . @Javier: By definition, the rank of a matrix is the dimension off the span of its rows (which is equal to the dimension of the span of its columns); elementary row operations do not change the row space, so doing Gaussian elimination does not change the rank, it only makes it easier to tell what the rank is (if you are doing it correctly, at any rate) In summary: yes, because you are
factorial - Why does 0! = 1? - Mathematics Stack Exchange Intending on marking as accepted, because I'm no mathematician and this response makes sense to a commoner However, I'm still curious why there is 1 way to permute 0 things, instead of 0 ways