Pi notation question.

Hi Max

I'm with GingerAle, the expression after the Big Pi is equal to a+b when c = 0, it's equal to a+b when c = 1, it's equal to a+b when c = 2, and so on all the way upto c = n. The product of all of those will be (a + b)^(n+1).

There has to be something wrong though since the largest power of a on the lhs is 2n, while on the rhs it's n+2.

HI Max,

Think of the “C” as a control variable for the index -- it keeps track of the iteration count.. These are not always part of the equation.  In this case (a+b) are multiplied to themselves (n+1) times.

BTW, when used in this context “Pi”  is known as “Big Pi.”

GA

Thanks Alan and GingerAle :)

Btw what is the correct general formula? :)

I have having problem with this pi notation.

I saw this on Internet: \(a^{2n} - b^{2n} = (a-b)[\displaystyle\prod^{n}_{c=0}(a+b)]\)

I know the Pi notation means product, but the expression after the Pi notation doesn't have the variable 'c' in it,

so how does that Pi notation work??

Algebraic Identity:

\(\begin{array}{|rcll|} \hline a^{n}-b^{n} &=& \displaystyle (a-b) \left[ \sum\limits_{k=0}^{n-1} a^{n-1-k}\cdot b^{k} \right] \\ \text{or} \\ a^{2n}-b^{2n} &=& \displaystyle (a-b) \left[ \sum\limits_{k=0}^{2n-1} a^{2n-1-k}\cdot b^{k} \right] \\ \hline \end{array} \)

For Example:

\(\begin{array}{|rcll|} \hline a^2-b^2 &=& (a-b)\cdot (a+b) \\ a^3-b^3 &=& (a-b)\cdot (a^2+ab+b^2) \\ a^4-b^4 &=& (a-b)\cdot (a^3+a^2b+ab^2+b^3) \\ \hline \end{array}\)