Does anybody know where I can find a general form, in terms of n, of the sum $\left(\sum\limits_{i=1}^n a_i\right)^n$. What I mean is, there appears to be some sort of pattern, if you look at $\left(\sum\limits_{i=1}^2 a_i\right)^2$ you get $a_1^2+2a_1a_2+a_2^2$ and if you let $n=3$ then you get $a_1^3+a_2^3+a_3^3+3a_1^2(a_2+a_3)+3a_2^2(a_1+a_3)+3a_3^2(a_2+a_3)+6a_1a_2a_3$. I'm working with something right now where I'd like to subtract out the cubed terms and have a general formula left over for the remaining terms which I can write simply in terms of $n$. Sorry about the lack of clarity, I hope this helps.
Tell me more
×
Mathematics Stack Exchange is a question and answer site for
people studying math at any level and professionals in related fields. It's 100% free, no registration required.
|
|
It isn't really clear what you are asking. Perhaps this will help: http://en.wikipedia.org/wiki/Multinomial_theorem |
|||||
|
