How do learn how to add the numbers 1 - 100 in 3 seconds? I mean like 1+2+3+4+5+6+7+8+9+10....................

Answer 1

It's all about seeing patterns in series of numbers. One history of this particular summation is credited to the mathematician Gauss when he was about ten years old. According to the story, his teacher wanted to keep his class busy and asked them to add up the numbers from one to one hundred, expecting that it would take them some time. Young Gauss saw a pattern and had the answer in a few seconds.

The pattern that he saw was this: take the first and last number in the list of numbers to add up (1 and 100). Their sum is 101. Now look at the second and second last numbers: (2 and 99). Their sum is also 101. There are fifty such pairs in the list, each of which sum to 101, so the sum of the whole list is 50*101=5050.

The general formula is n/2*(n+1) or n*(n+1)/2. It works even when n is odd. (See if you can reason out why!)

The ancient Greeks also knew about this formula, but at least according to the story, young Gauss figured it out on his own.

Answer 2

9. change the fractions so they have the same denominator so 6 2/8 + 1 5/8 + 4 4/8 = 11 11/8 = 12 3/8 ---> 8/8 is one and 3 left over 10. 27 divided by 1 1/5 make it a standard fraction 1 1/5 is 6/5 so it would be 27/6/5 which is the same thing as 27/1 * 5/6 which is 27 *5 over 6 * 1 = 135/6 = 22.5 11. 3/10 divided by 3/4 is the same thing as 3/10 multiplied by 4/3 3/10 * 4/3 -- just multiply the top and bottoms--- 12/30 = 4/10 12. This would be easier to make standard fractons 1st 10 1/4 is the same thing as 41/4 and 7 1/3 is the same thing as 22/3 so now you have 41/4 - 22/3 -- make it the same denominator --- 123/12 - 88/12 = 35/12 or 2 11/12 13. 21/5 * 10/3 = 210/15 = 14 14. 5/2 + 3/2 = 7/2 15. 1/6 * 30 = 30/6 = 5 16. 8/4 - 7/4 = 1/4 22. 2/3 = n/12 multiply by 12 and you get 12*2/3 = n which is 24/3 = n n= 8 23. just divide on ur calc or see that 4/5 is the same thing as 8/10 or .8 24. same thing 3/4 on ur calc is .75 --> multiply by 100 and you get 75 thats the percentage -- 75% or you can figure out how man times 4 goes into 100 which woudl be 25 and multiply by 3 and get 75 percent that way 25. 1 1/2 is the same thing as 1 hr and 30 minutes -- theres 60 minutes in an hour so an 60 and 30 and get 90 minutes 26. theres a 100 centimeters in a meter -- so if you have half a meter thats half a 100 or 50 --- 50 centimeters in half a meter 28 take .20 and multiply by 120 on ur calc to get the decimal just take the percentage 20% and divide by 100-- you get .20 - multiply by 120 or you can recognize that 1/5 is 20% and take 1/5 * 120 which is 120/5 and get 24

Answer 3

u can do it fast but whether u can do it within 3 seconds is another question by itself.

add the 1st number(1) to the last number(100) and you get 101. do the same for 2nd number(2) and 2nd last number(99) and you still get 101. u will find that as you carry on, you will reach the 50th number(50) and the 50th last number(51). Since you have 50 sets of 101, the sum of 1 - 100 = 50 x 101 = 5050.

alternatively, you may try using a calculator.

hope this helps=)

Answer 4

You can never do this in 3 seconds, but 5 seconds maybe =P.
Gauss solved this through logic when he was a little toddler! He was like, "Hmm, 100+1=101, 99+2=101,... So then 101*50 is the answer! Yay I'm a child prodigy!" The answer is 5050. Here's the story why he started solving it. His teacher tried to keep the kids occupied so he or she gave them a question. Add all the integers from 1-100. Bazaam goes Gauss and he knocked his teacher out with the mightest words! 5050... The strength of numbers is not to be underestimated. Speech is your sword.

Answer 5

Gauss did this when he was a child by
adding 0 + 100 = 100
to 1 + 99 = 100
2 + 98 = 100
and then he thought he could do that up to
49 + 51 = 100
so he would have 50 hundreds which is 5000, but
then he had that extra 50 which makes it 5050

the formula now is
Using capital S as the sum
and n as the number of numbers
a1 as the beginning number and an as the ending number

S = n(a1 + an)/2

Answer 6

Two ways:
If 1 is the first number, 100 is the last number, then the sum is 100*101/2

The sum of 1+100 is 101, so is 2+99, etc. You have 50 such pairs.

Answer 7

Carl Gauss figured this one out. Imagine that the numbers from 1 to 50 are listed in one column, and the numbers 51 to 100 are listed in an adjacent column, in reverse order. The sum of the two numbers in any row is 101, and there are 50 rows, so the sum of all the numbers is 5050.

Answer 8

1+ 2+ 3 + ... + 99 + 100

+

100 + 99 +98 + ... + 2 + 1

=

100 * 101 = 10100


now jus tdivide by 2 (because you've added two sumations)

10100 / 2 = 5050

Answer 9

You group 0 and 100, 1 and 99,..., 49 and 51 plus 50
= 5000+50 = 5050

Answer 10

Already know...
The sum of the first N numbers is (N)(N+1)/2
So, 1+....+ 100 = 50*101 -r 5050


Or did you have another trick.