CSC300 / CSC402: Adding up an arithmetic series [1/7] Previous pageContentsNext page

Suppose we add up the elements we get counting by adding 1:

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + ... + N

Let's count to 16!

01 
02 02 
03 03 03 
04 04 04 04 
05 05 05 05 05 
06 06 06 06 06 06 
07 07 07 07 07 07 07 
08 08 08 08 08 08 08 08 
09 09 09 09 09 09 09 09 09 
10 10 10 10 10 10 10 10 10 10 
11 11 11 11 11 11 11 11 11 11 11 
12 12 12 12 12 12 12 12 12 12 12 12 
13 13 13 13 13 13 13 13 13 13 13 13 13 
14 14 14 14 14 14 14 14 14 14 14 14 14 14 
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 
16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 

You get a triangle, which is half of a square.

The sum is approximately N squared divided by 2.

0 + 1 + 2 + 3 + 4 + ... + N = (N^2)/2 + N/2

Why add N/2?

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