- #1

- 17

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[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. :)

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- 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. :)

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- #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 + ...

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