Properties of summation notation, Mathematics

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Properties

Now there are a couple of formulas for summation notation.

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here c is any number. Therefore, we can factor constants out of a summation.

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Therefore we can break up a summation across a sum or difference.

Consider that we started the series at i₀ to denote the fact as they can begin at any value of i which we require them to. Also consider that whereas we can break up sums and differences whereas we did in 2 above we cannot do similar thing for products and quotients. Though,

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