you can use product or palettes

fantasy — Sun, 03 Oct 2010 18:41:02 Z

I think it's simple,

product(i^k, k = 1 .. 2010)

yield which you want.

homework

pagan — Sun, 03 Oct 2010 19:03:22 Z

This looks like homework.

Since Maple can just give you the answer (which really won't help you understand how it works) then maybe it's ok to explain.

Ask youself why this formula works:

> product(i^k,k=1..N);
                  /           2              \
                  \1/2 (N + 1)  - 1/2 N - 1/2/
                 i

Let's simplify that a bit, to make it more legible.

> simplify(%,power,size);
                         (1/2 N (N + 1))
                        i

Do you understand that you can add exponents when taking a product? I think it's likely that you are supposed to use the formula for sum(k,k=1..N). Have you studied that?

> simplify(sum(k,k=1..N),size);
                          1          
                          - N (N + 1)
                          2

Once you know that, and if you know how to combine exponents of products using addition, you can get here.

> i^((2010*(2010+1))/2);
                             2021055
                            i       

> i^sum(k,k=1..2010);
                             2021055
                            i       

> product(i^k,k=1..2010);
                             2021055
                            i

Does that make sense to you?

(For the Maple purists, yes, `add` and `mul` could be used instead of `sum` and `product` in those last two results involving a finite number of terms. But using so many command names might make it more confusing.)

i

Robert Israel — Mon, 04 Oct 2010 09:07:49 Z

I have only one thing to add to Pagan's excellent answer: if your i is supposed to be a square root of -1, in Maple that is I rather than i.

MaplePrimes - answers and comments on Question, How can I calculate this product?

you can use product or palettes

homework

i