2006-09-12 23:45:42 · 12 answers · asked by Anonymous in Education & Reference ➔ Quotations
Instead of adding like this...
1 + 2 + 3 + . . . . + 99 + 100 = ?
It is much faster to add like this...
(1 + 100) + (2 + 99) + (3 + 98) + . . . . + (50 + 51) = ?
Every pair of numbers adds up to 101. There are 50
pairs of numbers, so the answer is 50x101 = 5050. Of course According to Gauss, this method is about 20 times faster than other methods.
2006-09-13 00:07:10 · answer #1 · answered by Katie 2 · 0⤊ 0⤋
you could use the fact that other than 100 - there are 'pairs of numbers' that all add to 100 = ie 1+99, 2+98, 3+97...25+75, 26+74...33+67, 34+66, 35+65,... and so on all the way to 49+51...
count all these pairs - that 49 pairs all adding to 100 - with only the numbers 50 and 100 left (if you are including 100 itself in the sum) therefore 49x100=4900 plus 50 plus 100= 5050...which I guess is the sum
2006-09-13 06:53:39 · answer #2 · answered by websage 4 · 0⤊ 0⤋
The fast way is to add the numbers that add to 100, like 1+99, 2+98, 3+97, etc. The only number left will be fifty... and you tack that on the end
2006-09-13 06:49:44 · answer #3 · answered by girl_alphabet 2 · 0⤊ 0⤋
x(x + 1)/2
eg 7 x (7 + 1)/2 = 28
7 + 6 + 5 + 4 + 3 + 2 + 1 = 28
Similarly: 100 x (100 + 1)/2 = 5050
2006-09-13 07:52:02 · answer #4 · answered by verne 2 · 2⤊ 0⤋
There's a quicker way. With an even number of consecutive digits there are two numbers in the middle - in this case 50 and 51. The midpoint between this two is 50.5 which is the average of that number sequence. Multiply that average by the number of digits (100 in this case), and you have your answer.
100 X 50.5 = 5,050.
If there had been an odd number of consecutive digits, as with numbers 1 to 99, then there is just one central number: 50. When you multiply this by the number of digits you have the answer. Hence 99 X 50 = 4,950.
2006-09-13 07:05:36 · answer #5 · answered by ♫ Rum Rhythms ♫ 7 · 1⤊ 0⤋
find the number of pairs of numbers there are in the series
(max number - min number)/2 = No of sets
(100-1)/2 = 50
add together the highest and the lowest number
100+1 = 101
and multiply by the number of sets
101 * 50 = 5050
this works for any set which increments by 1, you will need a different formula if the interval is not 1
2006-09-13 07:22:49 · answer #6 · answered by Mark J 7 · 0⤊ 0⤋
1 2 miss afew 99 100 lol
2006-09-13 06:55:23 · answer #7 · answered by Anonymous · 0⤊ 0⤋
An excell spreadsheet
Aswer = 5050 (inclusive of 1 and 100)
2006-09-13 06:47:11 · answer #8 · answered by PollyPocket 4 · 0⤊ 0⤋
As PollyPocket said Excel is a 2 second jobbie
2006-09-13 06:54:35 · answer #9 · answered by Farmer Phil 2 · 0⤊ 0⤋
definately an excell spreadsheet as Polly says
2006-09-13 06:56:13 · answer #10 · answered by Anonymous · 0⤊ 0⤋