Saturday, 1 August 2009

Sum of the first ½ integer

This may not make sense. There is ½ of an integer, but what is the first ½? 

Just consider this formula sn(n+1), which gives the sum of the first n integers, s. When we plot a graph of s versus n, we have

From the graph, the s value will give the sum of the first n integer. Like reading off from the graph. So to find the sum of the first ½ integer, just substitute n=1/2 and we have s = 3/8. This applies to any fraction.

Ya the sum of the first ½ integer is 3/8. It is by no means any serious mathematics. Just some food for thought.

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