Consider the problem of adding a group of consective numbers such as: 1, 2, 3, 4, 5, 6, 7, 8, and 9. How would you go about finding their sum ?
This group is certainly easy enough to add the usual way.
But if you're really clever you might notice that the first number, 1, added to the last number , 9, totals 10 and the second number, 2, plus the next to last number, 8, also totals 10.
In fact, starting from both ends and adding pairs, the total in each case is 10. We find there are four pairs, each adding to 10; there is no pair for the number 5.
Thus 4 x 10 = 40 ; 40 + 5 = 45
Going a step further, we can develop a method for finding the sum of as many numbers in a row as we please
Going a step further, we can develop a method for finding the sum of as many numbers in a row as we please
Rule : Muliply the amount of numbers in the group by one more than their number , and divide by 2.
As an example , suppose we are asked to find the sum of all numbers from 1 to 99. There are 99 intergers in this series : one more than this is 100 . thus
99 X 100 = 9,900
9,900 / 2 = 4,950 Answer
The sum of all nimbers from 1 to 99 is therefore 4,950.
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