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The answer is 5050.

One way to see how to get the answer is as follows:

Suppose

S = 1 + 2 + 3 + . . . + 100

Then, rewriting it another way,

S = 100 + 99 + 98 + . . . + 1

Now the sum of each number and the one below it is 101 and there are 100 such pairs.

So

2*S = 101 + 101 + 101 + . . . + 101 (100 entries)

2*S = 100*(100+1)

So S = 100*(100+1)/2 = 50*101 = 5050

Q: How do you add numbers 1-100?

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