2006-09-20 23:31:44 · 8 answers · asked by angel 1 in Science & Mathematics ➔ Mathematics
I'll give you more than the formula, I will show you how to derive it.
If you add numbers from 1 to n, the total is n(n+1)/2.
How do we know that? Because you can add n to 1, and (n-1) to 2 and so on, so you have n/2 values each totalling n+1 (it works even if n is odd, as you would have a half total left in the end).
Now, you want to add only the even integers, let's say from 1 to m.
You can say that m is the same as 2n throughout.
So the total of the first m even integers should be the same as twice the total of the first n integers, or n(n+1), and since we postulated that m=2n, the total is thus m/2(m/2+1).
Same way, if we want to add only the odd numbers, we can say that m is 2n-1 (if we said 2n+1, we'd miss 1 and we'd start at 3). Or, we can simply use the even total equation abive and subtract 1 for each value added up (so that 2 becomes 1, 4 becomes 3 and so on) that is to say n value less. If you work up the algebra, you end up with an interesting property: the equation reduces to a very neat ((m+1)/2)^2, that is the total of all the odd number from 1 to 7 is (8/2) ^2 or 16. Try it.
2006-09-20 23:39:41 · answer #1 · answered by Vincent G 7 · 4⤊ 3⤋
Sum Of Odd Numbers
2016-11-07 09:39:35 · answer #2 · answered by mccranie 4 · 0⤊ 0⤋
Sum Of Even Numbers
2016-12-29 11:52:12 · answer #3 · answered by deweese 3 · 0⤊ 0⤋
This Site Might Help You.
RE:
formula of sum of odd intergers,and formula of sum of even numbers?
2015-08-07 09:57:22 · answer #4 · answered by Anonymous · 1⤊ 0⤋
Suppose a quadratic whose difference in evaluates, from x to (x-1) form the sequence of odd integers. A particular one is x^2 - 58x + 841. It has its minimum at (x=29,y=3). (x=28,y=4),(x=27,y=7),(x=26,y=12)... The difference in terms are 4-3=1, 7-4=3, 12-7=5...
Thus the sum is the change in y, or f(29-n), n the number of odd terms in sequence.
Evaluate the quadratic (29-n)^2 -58(29-n) + 841.
(841 - 58n + n^2) - (1682 - 58n) + 841. Collecting terms resolves n^2, the sum of the sequence.
2014-01-09 09:56:14 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Sum of odd numbers = n^2
Sum of Even numbers = n(n+1)
2006-09-21 00:18:34 · answer #6 · answered by c2 brahmin 2 · 4⤊ 1⤋
The best
Sum of odd numbers = n^2
Sum of Even numbers = n(n+1)
2006-09-21 00:42:04 · answer #7 · answered by SAEED AHMAD 2 · 2⤊ 1⤋
even integers=n(n+1)
odd integers=n^2
2006-09-21 03:00:16 · answer #8 · answered by CHIMPU 2 · 1⤊ 0⤋
If you add the odd numbers 1,3,5,... upto n terms, you get n^2
If you add the even numbers 2,4,6,... upto n terms, you get n(n+1)
2006-09-20 23:39:17 · answer #9 · answered by astrokid 4 · 3⤊ 0⤋