Best Answer

The formula is:

S_n = (n(n+1))/2

where S is the sum and n is the amount of numbers (starting at 1).

So for 100:

S_100 = (100(101))/2 = 50(101) = 5050

Alternatively, you could group 0+100 (0 isn't a counting number, just a placeholder), 1+99, 2+98, ..., 49+51, 50. You get 50 groups of 100 and 1 of 50. 50(100) + 50 = 5050. I think this is what Gauss did.

Q: How do you find a quick and easy method to compute the sum of the first 100 counting numbers?

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