What is the sum of all whole numbers from 1 to 100?

Answer 1

The total is 5050.

There are 49 pairs of numbers that equal 100 (1+99, 2+98...) and the other unpaired numbers are 50 and 100.

Similarly, you can add 1 to 100 you get 101, if you add 2 to 99 you get 101 if you do it all the way down to 50+51 there is 50 pairs of 101. Then you multiply 101 by 50 to get 5050.

The process:

• You are adding 1 + 2 + 3 + 4 + 5...+ 96 + 97 + 98 + 99 + 100. If you were adding some portion that began with a number other than 1, or if you were adding just odds or evens, the method would be different.
• Notice that the first and last numbers add up to 101 (1 + 100). So do the second and second-to-last (2 + 99). In fact, all of the numbers pair up like this, always adding up to 101.
• If you paired up the numbers this way, you'd have 50 pairs, which is half of 100. Each pair's sum is 101.
• The formula that summarizes this trick uses "n" to stand for the top number, in this case 100. N multiplied by (n + 1), divided by 2, gives you the answer. (100 x 101) / 2 is the same as 50 x 101. 50 x 101 = 5050.

Answer 2

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