What is the large lowercase $n$ symbol in math?

Question

What is $\prod$ and how can I use it? I have seen it used under numerous occasions and on the Desmos graphing calculator keyboard-menu. I could not get it to work, and wanted some pointers.

Does this answer your question? What does the $\prod$ symbol mean? — Benjamin Wang, Feb 18 '21 at 01:37
That is not an "n". That is a capital $\pi$ and means product. For example $\displaystyle \Pi_{j=1}^3 j = 1 \cdot 2 \cdot 3 = 6.$ — mjw, Feb 18 '21 at 01:37
@mjw : You are of course right about the origin of the symbol, but notice this difference: $$\begin{align} & \Pi_{i=1}^3 a_i \ {} \ & \prod_{i=1}^n a_i \end{align}$$ The first is coded as \Pi and the second as \prod, and the second is standard usage in mathematical notation. — Michael Hardy, Feb 18 '21 at 02:36
Well yes, \prod is better than \Pi here. Thanks for the prodding. — mjw, Feb 18 '21 at 02:51

score 4 · Accepted Answer · edited Feb 18 '21 at 02:37

4

As pointed out by multiple users above, this is the uppercase version of $\pi$ in the greek alphabet, and it usually means "product".

In Desmos, you use it like this, similar to the summation sign ($\Sigma$):

$$ \prod_{i=a}^b {c} $$

where $a$ is the lower bound (bound included), $b$ is the upper bound (bound included), and $c$ is the component to take the product of.

An example:

$$ \prod_{i=1}^{10} {(i+2)} = (1+2) \cdot(2+2) \cdot(3+2) \cdot(4+2) \cdot(5+2) \cdot(6+2) \cdot(7+2) \cdot(8+2) \cdot(9+2) \cdot(10+2)$$ $$ = 239500800 $$

Hope this helps.

edited Feb 18 '21 at 02:37

Michael Hardy

1

answered Feb 18 '21 at 01:51

Bryan351018

73

1

Nice answer but the product evaluates to $ 239500800$. If you perform all the additions, you get $34567891011*12 = 12!/2$ – Some Guy Feb 18 '21 at 02:30
1

Edited it in for you – Some Guy Feb 18 '21 at 02:34

score 3 · Answer 2 · answered Feb 18 '21 at 01:47

The Greek "S" is $\Sigma$ is typically used for sum. Analogously, The greek capital "P" is $\Pi$ and is typically used for product. We can use it to index some collection of numbers that we wish to multiply together. Say for example I wish to define $n! = n \cdot (n-1)\cdot (n-2)...\cdot 2\cdot 1$. I could write this as $\Pi_{k=1}^n k$ which says that we take every integer value $k$ between $1$ and $n$ and multiply them together.

What is the large lowercase $n$ symbol in math?

2 Answers2