The next step in our game of summation is to generalize formula (1). Instead of calculating the sum of numbers between 1 and n, we can calculate the sum of numbers between m and n:
(5)For m=1 formula (5) becomes formula (1):
Formula (5) can be transformed into:
(6)In order to calculate the numbers m and n, we'll show the number 2S as a product of factors P1 and P2:
(7)For the given number S, we can have more than one pair of numbers P1 and P2, depending on prime factors of the number S.
For example, for S = 78 we can write:
Since the numbers n+m and n-m+1 have different parity, we have the following cases:
|
a) m=78 n=78 |
b) m=25 n=27 |
c) m=18 n=21 |
d) m=1 n=12 |
Or:
Step 2
Graphing
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