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 Question from Mimi, a parent: Compute the following: 2,006-1-2-3-4-...-48-49-50

Hi Mimi,

You want to calculate

$2,006 -1 -2 -3 - \cdot \cdot \cdot -48 -49 -50 = 2,006 - (1 +2 +3 +\cdot \cdot \cdot + 48 +49 + 50)$

so the result is easily obtained if you can calculate

$1 +2 +3 +\cdot \cdot \cdot + 48 +49 + 50.$

To do this I would start at both ends and work towards the middle.

$1 + 50 = 51, 2 + 49 = 51, 3 + 48 = 51$

How many 51s are there? What is

$1 +2 +3 +\cdot \cdot \cdot + 48 +49 + 50?$

Penny

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