The easiest way to do this is to use a formula. This formula works together for adding all the numbers in a sequence of numbers starting at 1 and ending at n, regardless of the length of the sequence.

The formula is: n(n+1)/2

In your case, n = 100, so the formula becomes: 100 x 101 divided by 2 = 10100/2 = 5050

You can test it out with a smaller number, where it is easy to do the whole sum the long way in your head as a check. For example, to add up all numbers from 1 to 5 is 1+2+3+4+5 = 15

using the formula: 5 x 6 divided by 2 = 30/2 = 15

5050

it is easiest if you add the numbers in lots of 100 each.

Start with 1 + 99

then continue as follows

2 + 98

3 + 97

4 + 96...

and so on until you get to 49 as in

49 + 51

You now have 49 lots of 100 and the number 100 itself must be added so you now have

50 lots of 100 = 5000

Because this method leaves the number 50 as a single number you must add it too, giving a grand total of

5050.

The sum of the numbers through 1 to 100 is 5050. It can easily be calculated by the formula of the arithmetic progression, that is [n * (n + 1)] / 2. Here n is 100. By putting the value of n is the equation, we get

[ 100 * (100 +1)] / 2

= [ 100 * (101)] / 2

= 10100 / 2

= 5050 (Answer)

5050. 1+99,2+98 and so fort. You will get 5000. However in the number 100, there are 2x50. Therefore you can write it as 50x101 = 5050

...You just need to group the numbers from the sum that is

1+2+3+...+99+100=(1+100)+(2+99)+...+(50+51)=50x51=5050