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| Math Central | Quandaries & Queries |
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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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