Formula For Adding Sum To "N" Terms

Can you find a quick and elegant way to add the numbers from 1 to 30?

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

1 + 2 + 3 + ....... + 30 =

Solution:

Here's an elegant way:

1 + 30 = 31

2 + 29 = 31

3 + 28 = 31

.....................

.....................

15 + 16 = 31

Adding the above equations gives

1 + 2 + 3 + ....... + 30 = 15 × 31 = 465

Food for thought:

The general formula is:

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