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Can you find a quick and elegant way to add the numbers from 1 to 36 ?

In other words, what is the sum you obtain in the following case:

1 + 2 + 3 + ....... + 36 =
Answer: 666

Solution:

Here's an elegant way:

1 + 36 = 37
2 + 35 = 37
3 + 34 = 37
.....................
.....................
18 + 19 = 37

Adding the above equations gives

1 + 2 + 3 + ....... + 36 = 18 × 37 = 666

Food for thought:

The general formula is:

1 + 2 + 3 + ....... + n = n (n + 1) / 2.

Is the formula valid when n is an odd integer?

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puzzle : image for addition

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