Summation multiplication

Question

What is wrong with writing:

$\displaystyle \Sigma_{n}\ a_n .$ $\Sigma_{n}\ b_n$ ?

I understand that it does not matter what dummy variable you sum over, but I don't understand why this is seen as ambiguous

I don't like it, but there is only one reasonable interpretation. — André Nicolas, Feb 21 '16 at 00:01

score 1 · Answer 1 · answered Feb 21 '16 at 00:02

1

It is bad style. The scope of the variable $n$ occurs within the summations; it is a "local variable" to the looping processes of the sum. Wny not do this? It confuses others. It will also mislead you into doing dumb stuff. Take note of this. The equality $$\sum_n a_n \cdot \sum_n b_n = \sum_{m, n} a_m b_n$$ properly carries out the distrubutive law. Mixing the scopes of the two $n$ can result in disaster.

answered Feb 21 '16 at 00:02

ncmathsadist

49,383

Is $\sum_{m, n} a_m b_n \equiv \sum_{m}\sum_{n} a_m b_n$? – usainlightning Feb 21 '16 at 00:07
1

Yes. It is the distributive law. – ncmathsadist Feb 21 '16 at 00:23

Summation multiplication

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