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Properties
Now there are a couple of formulas for summation notation.
1.
here c is any number. Therefore, we can factor constants out of a summation.
2.
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,
Before searching at series solutions to a differential equation we will initially require to do a cursory review of power series. So, a power series is a series in the form, .
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