- #1

- 17

- 0

[itex]\left(\sum_{i=1}^{n}a_ib_i\right)\left(\sum_{i=1}^{k}a_ib_i\right)[/itex] where n,k are some positive integers.

I feel certain that it's not just a sum to n+k or nk, but I could be wrong. any help would be awesome. :)

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter praecox
- Start date

- #1

- 17

- 0

[itex]\left(\sum_{i=1}^{n}a_ib_i\right)\left(\sum_{i=1}^{k}a_ib_i\right)[/itex] where n,k are some positive integers.

I feel certain that it's not just a sum to n+k or nk, but I could be wrong. any help would be awesome. :)

- #2

- 27

- 0

The terms of the new series are the convolution of the original terms.

An elementary way to see it is: attach x^i to each coefficient, then group in a single series in powers of x, then put x=1.

Like you would do for (1 + x + 3 x^2)(2 + x + x^2)= (1+2) + (1*2+1*1)x + (3*2+1*1+1*1)x^2 + ...

Share: