The sum notation uses the capital Greek letter sigma as follows:
Thus if x1 = 6, x2 = 7 and x3 = -2, then
Note that index i can be replaced by any other index and the results will be the same. Thus,
Also, the initial value doesn’t have to be 1. For example, assuming k ≤ n
The initial value can also be –
We can iterate the use of the sigma notation. For example,
We can also use abbreviated notations such as the following:
There is a similar notation for products using the capital Greek letter pi:
I can’t seem to get it. Here is what I am trying to do.
a b c
0 0 0
1 3 3
2 6 9
3 9 18
For each iteration of a, b=+3 and c=b+c-1. i
Hi,
Is it possible to do the Capital Pi (Product) function on Excel?
Here is what I need to do, using an example with the first three rows (it will go up to 101 rows):
1st row Y_1=x_1 (1-z_1)
2nd row Y_2=x_2 (1-z_1)(1-z_2)
3rd row Y_3=x_3 (1-z_1)(1-z_2)(1-z_3)
Any advice would be greatly appreciated. Thank you!
Grace,
There is a product function in Excel that you could use. If R1 is a range then =PRODUCT(R1) returns the value which is the product of the values of all the cells in R1.
Charles
not helpful!
What changes would you like to see to make the information more helpful?
Charles
Any solutions founds on this?
Eduardo,
Sorry, but I don’t understand your question. What are you referring to?
Charles
Worked fine for me. I don’t know what your issue is angry economist but I found Charles’s advice to be spot on. The only area I can see it be slightly confusing is he referred to a range as R1, which in excel speak typically refers to the individual cell R1, but from the context he provided you can see that is not what he meant.
I didn’t find it helpful either, and assuming AE had the same problem as me, I can explain.
PRODUCT(RANGE) technically works fine, but it requires that you first set up the RANGE to contain all the individual iterations of the Pi Notation expression you’re trying to compute. Ideally, this is the step we would want to avoid by using Pi Notation in the first place.
I’m sure it’s possible to code up a functional analog in native VBA (which is what I’m probably going to end up doing), but I have to assume my problem isn’t novel, and someone has had the idea to do this before.
@Anonymous
You can generate a series using the =SEQUENCE() function. You can then throw that series into the =PRODUCT() formula.
If n is A3, =SEQUENCE(A3,1,1,1) generates a series containing {1,2,3,…,n}.
For example, =PRODUCT(SEQUENCE(A3,1,1,1)) is equivalent to n factorial.