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Title [Harim Yoo] The Essential Guide to Competition Math (Fundamentals): Topic 5, #19
The Essential Guide to Competition Math (Fundamentals) 31
Author alo*** Date Posted 2024-07-31 오전 10:05:16

Hi Mr. Yoo,


In the last step: 9(151+199)/2

Why are we dividing by 2? Could you elaborate on how the numbers we calculated are used in the last step please?


Thank you for your time!


P.S. Thanks for always being so thoughtful with all your replies, they truly help clarify! (My Korean's not the best, so sometimes I have difficulty understanding...)

2024-07-31 오전 10:59:31

Howdy!

 

Let's see what happens right here. We must add 151, 157, 163, ...., 199.

 

Think about a rainbow method that coonects 151 by 199, 157 by 193, and so on.

 

The sum 151+199 came out 4.5 times because we pair up 9 numbers, and the middle number comes out as its standalone. 

 

This is called an arithmetic series, and let me give you a formula.

 

x_1+x_2+x_3+...+x_n can be computed as n(x_1+x_n) / 2 

 

Thank you for listening to the lecture, and you are almost at the end of the lecture. Great! Keep up the good work, and ask me bunch of questions in geometry part as well!!

 

Yay!!

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