Register to reply

Sum of all possible products of elements taken from couples

Share this thread:
Dec13-13, 12:11 PM
P: 12

I have N couples of real numbers higher than 1.
Let's call them like (a0,b0), (a1,b1),...,(aN,bN)
I have a number R <= N.

I need the sum of all the possible products of N elements, chosing one from each couple but exactly R times the "b" element and N-R times the "a" element.
Which is the best way to do it?

As an example:
(2,3), (5,7), (11,13)
N = 3, R = 2
I need 2x7x13 + 3x5x13 + 3x7x11

Thank you!
Phys.Org News Partner Mathematics news on
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Iranian is first woman to win 'Nobel Prize of maths' (Update)
Dec13-13, 12:45 PM
1MileCrash's Avatar
P: 1,295
As an expression I think what you want to do is:

[itex]\Sigma^{N}_{k=0} (a_{k}(\Sigma^{N}_{i=0} b_{i}))[/itex]

I have no idea if there is any way to compute this other than just doing it.

EDIT: Nevermind, I see you don't want "sum of all possible products of N+1 elements" but sum of all possible products of a choice of R elements from the N+1 elements. No idea, you're probably going to have to write a program for that.
Dec17-13, 01:24 AM
P: 12
I got the answer from "Michael":
It is the coefficient of x^R in (a0+xb0)(a1+xb1)...(aN+xbN)

Register to reply

Related Discussions
Converting volume elements to area elements Calculus & Beyond Homework 2
Question: Can elements above iron actually be clusters of smaller elements? Atomic, Solid State, Comp. Physics 3
Kronecker product on only a few elements in a matrix: How to align resulting elements Linear & Abstract Algebra 0
Orders of products of group elements. Linear & Abstract Algebra 4
Questions concerning cross products, dot products, and polar coordinates Introductory Physics Homework 1