in other words what is the sum you obtain in the following case
1+2+3.........+36=
2007-01-19 07:17:54 · 8 answers · asked by Future doctor! 1 in Science & Mathematics ➔ Mathematics
I could tell ya but I dont think its elegant enough
2007-01-19 07:21:12 · answer #1 · answered by Anonymous · 0⤊ 3⤋
Take the first and last (1 + 36)
Then the second and 35th (2 + 35)
Then the third and 34th (3 + 34)
etc.
Each time the sum is 37. And you can pair them 18 ways (36/2).
So the answer is 18 x 37.
Okay, so you forgot your calculator and want to know the answer. Notice that 3 x 37 = 111.
So you have 6 x (3 x 37) = 6 x 111
You can quickly figure out in your head that the answer is:
6 x 111 = 666.
In general, the sum of the number 1 through n is given by the formula:
n (n + 1) / 2
= 36 (37) / 2
= 18 x 37
= 666
2007-01-19 15:23:29 · answer #2 · answered by Puzzling 7 · 3⤊ 0⤋
Lots of people know the formula n(n+1)/2...but not a lot of people know the easiest way to prove that it works.
Write the numbers from 1 to 36 forward and in reverse:
01 + 36 = 37
02 + 35 = 37
03 + 34 = 37
04 + 33 = 37
05 + 32 = 37
06 + 31 = 37
07 + 30 = 37
08 + 29 = 37
09 + 28 = 37
10 + 27 = 37
11 + 26 = 37
12 + 25 = 37
13 + 24 = 37
14 + 23 = 37
15 + 22 = 37
16 + 21 = 37
17 + 20 = 37
18 + 19 = 37
19 + 18 = 37
20 + 17 = 37
21 + 16 = 37
22 + 15 = 37
23 + 14 = 37
24 + 13 = 37
25 + 12 = 37
26 + 11 = 37
27 + 10 = 37
28 + 09 = 37
29 + 08 = 37
30 + 07 = 37
31 + 06 = 37
32 + 05 = 37
33 + 04 = 37
34 + 03 = 37
35 + 02 = 37
36 + 01 = 37
That's 36 rows of 37, for a total of 1,332. But doing it that way, you actually found twice as much as you were looking for, so the sum is 1,332/2 = 666...
Ick...mark of the beast...intentional?
2007-01-19 15:27:56 · answer #3 · answered by Jim Burnell 6 · 1⤊ 0⤋
1+2+3+ 36
36+35+34++++1 written in inverse order
.Sum up each column.You get always 37.
You have 36 sumands equal to 37 which is twice your sum.So
S = 36*37/2 =666
The general formula for the sum 1+2+3+.....+n=n*(n+1)/2
2007-01-19 15:28:05 · answer #4 · answered by santmann2002 7 · 1⤊ 0⤋
You can use the formula for the sum of the first n numbers is
n(n+1)/2
So the answer would be,
36(37)/2=666
2007-01-19 15:34:50 · answer #5 · answered by purpleraiment 2 · 1⤊ 0⤋
1+2+3.........+36=(36*37)/2 = 666
In general:
1+2+3.........+n = n(n+1)/2
2007-01-19 15:20:56 · answer #6 · answered by Phineas Bogg 6 · 2⤊ 0⤋
Use Excel and the formula .I was taught it but I do not remember right now.
2007-01-19 15:22:46 · answer #7 · answered by Aoiffe337 3 · 0⤊ 4⤋
Please correct me if I'm wrong but don't you do 36! on a scientific calculator?
2007-01-19 15:22:06 · answer #8 · answered by ? 5 · 0⤊ 4⤋