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It’s All About Perspective!

Posted Jan 20, 2022.

How would you solve this problem? What is the best way to add up 100 numbers in a row? For example 1 + 2 + 3…..all the way up to 100?

…Like most problems in life, it’s all about our perspective, and sometimes a shortcut is the “smarter” way to go. Also, as Stephen Covey wrote “begin with the end in mind” is the key to success.

Here’s a quick story I ran across you may find interesting.

In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: 1 + 2 + 3 + ... + 98 + 99 + 100 = 5,050. The smart aleck was Carl Friedrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you "fold" the series of numbers in the middle and add them in pairs—1 + 100, 2 + 99, 3 + 98, and so on—all the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50×101. The more general formula, for a list of consecutive numbers from 1 through n, is n(n + 1)/2. (Source: The American Scientist website)

You probably just think I’m a math nerd, but this can be applied to many things in life, not just math.

On a side note, we are giving away Utah Jazz tickets this month when you refer in a new friend or family member for a checkup, consultation or implant evaluation. To learn more visit pinecrestdds.com/giveaways.

Have a great week!

Dr. Tyler Williams

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