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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,
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Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5. Ans: 103, 108..........998 a + (n-1)d = 998
Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.
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